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An Introduction to Measure Theory

Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 1470466406
Total Pages : 206 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Introduction to Measure Theory by : Terence Tao

Download or read book An Introduction to Measure Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2021-09-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

Geometric Measure Theory

Author : Herbert Federer
Publisher : Springer
ISBN 13 : 3642620108
Total Pages : 694 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Geometric Measure Theory by : Herbert Federer

Download or read book Geometric Measure Theory written by Herbert Federer and published by Springer. This book was released on 2014-11-25 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a major treatise in mathematics and is essential in the working library of the modern analyst." (Bulletin of the London Mathematical Society)

The Last Full Measure

Author : Jeff Shaara
Publisher : Ballantine Books
ISBN 13 : 0345438507
Total Pages : 578 pages
Book Rating : 4.3/5 (454 download)

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Book Synopsis The Last Full Measure by : Jeff Shaara

Download or read book The Last Full Measure written by Jeff Shaara and published by Ballantine Books. This book was released on 2011-01-05 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Pulitzer prize–winning classic The Killer Angels, Michael Shaara created the finest Civil War novel of our time. The Last Full Measure tells the epic story of the events following the Battle of Gettysburg and brings to life the final two years of the Civil War. Jeff Shaara dramatizes the escalating confrontation between Robert E. Lee and Ulysses S. Grant—complicated, heroic, and deeply troubled men. For Lee and his Confederate forces, Gettysburg has been an unspeakable disaster, but he is determined to fight to the bitter end; he faces Grant, the decisive, hard-nosed leader the Union army so desperately needs in order to turn the tide of the war. From the costly Battle of the Wilderness to the agonizing seize of Petersburg to Lee’s epoch-making surrender at Appomattox, Shaara portrays the riveting conclusion of the Civil War through the minds and hearts of the individuals who gave their last full measure. BONUS: This edition includes an excerpt from Jeff Shaara's Blaze of Glory.

Measure, Integration & Real Analysis

Author : Sheldon Axler
Publisher : Springer Nature
ISBN 13 : 3030331431
Total Pages : 430 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Measure, Integration & Real Analysis by : Sheldon Axler

Download or read book Measure, Integration & Real Analysis written by Sheldon Axler and published by Springer Nature. This book was released on 2019-11-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/

Measure and Integral

Author : Richard Wheeden
Publisher : CRC Press
ISBN 13 : 1482229536
Total Pages : 289 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Measure and Integral by : Richard Wheeden

Download or read book Measure and Integral written by Richard Wheeden and published by CRC Press. This book was released on 1977-11-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given.

A Measure of Everything

Author : Marcus Weeks
Publisher : Richmond Hill, Ont. : Firefly Books
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis A Measure of Everything by : Marcus Weeks

Download or read book A Measure of Everything written by Marcus Weeks and published by Richmond Hill, Ont. : Firefly Books. This book was released on 2005 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive reference and history book on what is measured and why. Measurement is one of humankind's oldest and most vital activities. By measuring height, speed, size, temperature, strength and many other factors, humans can compare, improve and progress. In fact, measurement is an essential tool for survival. A Measure of Everything is a wide-ranging and comprehensive guide to what is measured and why. The book begins when the basic measurements were as simple as more, less and enough. As societies evolved, relative measurements were no longer sufficient. Advances in language allowed more precise measurements. Short distances were measured in relation to parts of the human body. For example, the ancient measurement cubit was the length of a pharaoh's arm plus the width of his hand. As society and culture progress and change, so do measurements. The rise of astronomy and the sciences demanded more exact measurements. These measurements are typically named after the discovering scientist, e.g., henry, curie, watt, rutherford, fahrenheit. This book features 28 categories organized into three sections: Earth and Life Sciences: astronomy, distance, time, meteorology, medicine, and five others. Physical Sciences: chemistry, mathematics, physics, speed, weight, temperature, and three others. Technology and Leisure: computers, engineering, finance, food, textiles, and four others. A Measure of Everything is an informative and entertaining book that will appeal to a wide range of readers.

The Last Full Measure

Author : Jack Campbell (Naval officer)
Publisher :
ISBN 13 : 9781596065680
Total Pages : 0 pages
Book Rating : 4.0/5 (656 download)

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Book Synopsis The Last Full Measure by : Jack Campbell (Naval officer)

Download or read book The Last Full Measure written by Jack Campbell (Naval officer) and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In a transformed mid-nineteenth century America dominated by plantation owners and kept in line by Southern military forces, a mild-mannered academic from Maine, Professor Joshua Chamberlain, stands accused of crimes against the nation. In court alongside him is Abraham Lincoln, whose fiery rhetoric brands him a 'threat to the security of the United States of America.' Convicted, Chamberlain is sentenced to forty years hard labor, while Lincoln s fate is indefinite detention at Fortress Monroe. But Professor Chamberlain then encounters military minds who understand the true ideals upon which the country was founded and who want to foment revolution. To succeed, they need a leader, someone to inspire the people to take up the cause of liberty: Lincoln. All they have to do is flawlessly execute a daring plan to rescue him from the darkest federal prison"--Jacket.

How Will You Measure Your Life? (Harvard Business Review Classics)

Author : Clayton M. Christensen
Publisher : Harvard Business Review Press
ISBN 13 : 1633692574
Total Pages : 26 pages
Book Rating : 4.6/5 (336 download)

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Book Synopsis How Will You Measure Your Life? (Harvard Business Review Classics) by : Clayton M. Christensen

Download or read book How Will You Measure Your Life? (Harvard Business Review Classics) written by Clayton M. Christensen and published by Harvard Business Review Press. This book was released on 2017-01-17 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the spring of 2010, Harvard Business School’s graduating class asked HBS professor Clay Christensen to address them—but not on how to apply his principles and thinking to their post-HBS careers. The students wanted to know how to apply his wisdom to their personal lives. He shared with them a set of guidelines that have helped him find meaning in his own life, which led to this now-classic article. Although Christensen’s thinking is rooted in his deep religious faith, these are strategies anyone can use. Since 1922, Harvard Business Review has been a leading source of breakthrough ideas in management practice. The Harvard Business Review Classics series now offers you the opportunity to make these seminal pieces a part of your permanent management library. Each highly readable volume contains a groundbreaking idea that continues to shape best practices and inspire countless managers around the world.

How to Measure Anything

Author : Douglas W. Hubbard
Publisher : John Wiley & Sons
ISBN 13 : 1118836448
Total Pages : 432 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis How to Measure Anything by : Douglas W. Hubbard

Download or read book How to Measure Anything written by Douglas W. Hubbard and published by John Wiley & Sons. This book was released on 2014-02-24 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now updated with new measurement methods and new examples, How to Measure Anything shows managers how to inform themselves in order to make less risky, more profitable business decisions This insightful and eloquent book will show you how to measure those things in your own business, government agency or other organization that, until now, you may have considered "immeasurable," including customer satisfaction, organizational flexibility, technology risk, and technology ROI. Adds new measurement methods, showing how they can be applied to a variety of areas such as risk management and customer satisfaction Simplifies overall content while still making the more technical applications available to those readers who want to dig deeper Continues to boldly assert that any perception of "immeasurability" is based on certain popular misconceptions about measurement and measurement methods Shows the common reasoning for calling something immeasurable, and sets out to correct those ideas Offers practical methods for measuring a variety of "intangibles" Provides an online database (www.howtomeasureanything.com) of downloadable, practical examples worked out in detailed spreadsheets Written by recognized expert Douglas Hubbard—creator of Applied Information Economics—How to Measure Anything, Third Edition illustrates how the author has used his approach across various industries and how any problem, no matter how difficult, ill defined, or uncertain can lend itself to measurement using proven methods.

The Measure of All Things

Author : Ken Alder
Publisher : Simon and Schuster
ISBN 13 : 074324902X
Total Pages : 432 pages
Book Rating : 4.7/5 (432 download)

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Book Synopsis The Measure of All Things by : Ken Alder

Download or read book The Measure of All Things written by Ken Alder and published by Simon and Schuster. This book was released on 2014-07-29 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: In June 1792, amidst the chaos of the French Revolution, two intrepid astronomers set out in opposite directions on an extraordinary journey. Starting in Paris, Jean-Baptiste-Joseph Delambre would make his way north to Dunkirk, while Pierre-François-André Méchain voyaged south to Barcelona. Their mission was to measure the world, and their findings would help define the meter as one ten-millionth of the distance between the pole and the equator—a standard that would be used “for all people, for all time.” The Measure of All Things is the astonishing tale of one of history’s greatest scientific adventures. Yet behind the public triumph of the metric system lies a secret error, one that is perpetuated in every subsequent definition of the meter. As acclaimed historian and novelist Ken Alder discovered through his research, there were only two people on the planet who knew the full extent of this error: Delambre and Méchain themselves. By turns a science history, detective tale, and human drama, The Measure of All Things describes a quest that succeeded as it failed—and continues to enlighten and inspire to this day.

Measure Theory and Integration

Author : G De Barra
Publisher : Elsevier
ISBN 13 : 0857099523
Total Pages : 240 pages
Book Rating : 4.8/5 (57 download)

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Book Synopsis Measure Theory and Integration by : G De Barra

Download or read book Measure Theory and Integration written by G De Barra and published by Elsevier. This book was released on 2003-07-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text approaches integration via measure theory as opposed to measure theory via integration, an approach which makes it easier to grasp the subject. Apart from its central importance to pure mathematics, the material is also relevant to applied mathematics and probability, with proof of the mathematics set out clearly and in considerable detail. Numerous worked examples necessary for teaching and learning at undergraduate level constitute a strong feature of the book, and after studying statements of results of the theorems, students should be able to attempt the 300 problem exercises which test comprehension and for which detailed solutions are provided. Approaches integration via measure theory, as opposed to measure theory via integration, making it easier to understand the subject Includes numerous worked examples necessary for teaching and learning at undergraduate level Detailed solutions are provided for the 300 problem exercises which test comprehension of the theorems provided

A User-Friendly Introduction to Lebesgue Measure and Integration

Author : Gail S. Nelson
Publisher : American Mathematical Soc.
ISBN 13 : 1470421992
Total Pages : 233 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A User-Friendly Introduction to Lebesgue Measure and Integration by : Gail S. Nelson

Download or read book A User-Friendly Introduction to Lebesgue Measure and Integration written by Gail S. Nelson and published by American Mathematical Soc.. This book was released on 2015-11-09 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: A User-Friendly Introduction to Lebesgue Measure and Integration provides a bridge between an undergraduate course in Real Analysis and a first graduate-level course in Measure Theory and Integration. The main goal of this book is to prepare students for what they may encounter in graduate school, but will be useful for many beginning graduate students as well. The book starts with the fundamentals of measure theory that are gently approached through the very concrete example of Lebesgue measure. With this approach, Lebesgue integration becomes a natural extension of Riemann integration. Next, -spaces are defined. Then the book turns to a discussion of limits, the basic idea covered in a first analysis course. The book also discusses in detail such questions as: When does a sequence of Lebesgue integrable functions converge to a Lebesgue integrable function? What does that say about the sequence of integrals? Another core idea from a first analysis course is completeness. Are these -spaces complete? What exactly does that mean in this setting? This book concludes with a brief overview of General Measures. An appendix contains suggested projects suitable for end-of-course papers or presentations. The book is written in a very reader-friendly manner, which makes it appropriate for students of varying degrees of preparation, and the only prerequisite is an undergraduate course in Real Analysis.

The Last Full Measure

Author : Michael Stephenson
Publisher : Crown Publishing Group (NY)
ISBN 13 : 0307395847
Total Pages : 482 pages
Book Rating : 4.3/5 (73 download)

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Book Synopsis The Last Full Measure by : Michael Stephenson

Download or read book The Last Full Measure written by Michael Stephenson and published by Crown Publishing Group (NY). This book was released on 2012 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considers how soldiers through the ages have met their deaths in times of war, covering such subjects as weapons and battlefield strategies while offering insight into cultural differences and the nature of military combat.

Introduction to Measure Theory and Integration

Author : Luigi Ambrosio
Publisher : Springer Science & Business Media
ISBN 13 : 8876423869
Total Pages : 193 pages
Book Rating : 4.8/5 (764 download)

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Book Synopsis Introduction to Measure Theory and Integration by : Luigi Ambrosio

Download or read book Introduction to Measure Theory and Integration written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2012-02-21 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra. All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book.

Measure Theory

Author : Vladimir I. Bogachev
Publisher : Springer Science & Business Media
ISBN 13 : 3540345140
Total Pages : 1075 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Measure Theory by : Vladimir I. Bogachev

Download or read book Measure Theory written by Vladimir I. Bogachev and published by Springer Science & Business Media. This book was released on 2007-01-15 with total page 1075 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.

Measure Theory and Integration

Author : M.M. Rao
Publisher : CRC Press
ISBN 13 : 1482258102
Total Pages : 790 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Measure Theory and Integration by : M.M. Rao

Download or read book Measure Theory and Integration written by M.M. Rao and published by CRC Press. This book was released on 2018-10-03 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications. With more than 170 references for further investigation of the subject, this Second Edition provides more than 60 pages of new information, as well as a new chapter on nonabsolute integrals contains extended discussions on the four basic results of Banach spaces presents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties details the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functions covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory Measure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines.

Measure for Measure

Author : William Shakespeare
Publisher : Cambridge University Press
ISBN 13 : 0521854482
Total Pages : 84 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Measure for Measure by : William Shakespeare

Download or read book Measure for Measure written by William Shakespeare and published by Cambridge University Press. This book was released on 2006-07-06 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the rediscovery of Elizabethan stage conditions early this century, admiration for Measure for Measure has steadily risen. It is now a favorite with the critics and has attracted widely different styles of performance. At one extreme the play is seen as a religious allegory, at the other it has been interpreted as a comedy protesting against power and privilege. Brian Gibbons focuses on the unique tragi-comic experience of watching the play, the intensity and excitement offered by its dramatic rhythm, the reversals and surprises that shock the audience even to the end. The introduction describes the play's critical reception and stage history and how these have varied according to prevailing social, moral and religious issues, which were highly sensitive when Measure for Measure was written, and have remained so to the present day.