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Measure Theory and Fine Properties of Functions

Author : LawrenceCraig Evans
Publisher : Routledge
ISBN 13 : 1351432834
Total Pages : 288 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Measure Theory and Fine Properties of Functions by : LawrenceCraig Evans

Download or read book Measure Theory and Fine Properties of Functions written by LawrenceCraig Evans and published by Routledge. This book was released on 2018-04-27 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions). Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.

Measure Theory and Fine Properties of Functions, Revised Edition

Author : Lawrence Craig Evans
Publisher : CRC Press
ISBN 13 : 1482242397
Total Pages : 313 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Measure Theory and Fine Properties of Functions, Revised Edition by : Lawrence Craig Evans

Download or read book Measure Theory and Fine Properties of Functions, Revised Edition written by Lawrence Craig Evans and published by CRC Press. This book was released on 2015-04-17 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measure Theory and Fine Properties of Functions, Revised Edition provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract

Measure Theory and Fine Properties of Functions, Revised Edition

Author : LAWRENCE CRAIG. GARIEPY EVANS (RONALD F.)
Publisher :
ISBN 13 : 9781138582491
Total Pages : pages
Book Rating : 4.5/5 (824 download)

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Book Synopsis Measure Theory and Fine Properties of Functions, Revised Edition by : LAWRENCE CRAIG. GARIEPY EVANS (RONALD F.)

Download or read book Measure Theory and Fine Properties of Functions, Revised Edition written by LAWRENCE CRAIG. GARIEPY EVANS (RONALD F.) and published by . This book was released on 2023 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Measure Theory and Fine Properties of Functions

Author : LawrenceCraig Evans
Publisher : Routledge
ISBN 13 : 1351432826
Total Pages : 227 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Measure Theory and Fine Properties of Functions by : LawrenceCraig Evans

Download or read book Measure Theory and Fine Properties of Functions written by LawrenceCraig Evans and published by Routledge. This book was released on 2018-04-27 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions). Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.

Notes on Real Analysis and Measure Theory

Author : Alexander Kharazishvili
Publisher : Springer Nature
ISBN 13 : 3031170334
Total Pages : 256 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Notes on Real Analysis and Measure Theory by : Alexander Kharazishvili

Download or read book Notes on Real Analysis and Measure Theory written by Alexander Kharazishvili and published by Springer Nature. This book was released on 2022-09-23 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.

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.

Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients

Author : Haesung Lee
Publisher : Springer Nature
ISBN 13 : 9811938318
Total Pages : 139 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients by : Haesung Lee

Download or read book Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients written by Haesung Lee and published by Springer Nature. This book was released on 2022-08-27 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides analytic tools to describe local and global behavior of solutions to Itô-stochastic differential equations with non-degenerate Sobolev diffusion coefficients and locally integrable drift. Regularity theory of partial differential equations is applied to construct such solutions and to obtain strong Feller properties, irreducibility, Krylov-type estimates, moment inequalities, various types of non-explosion criteria, and long time behavior, e.g., transience, recurrence, and convergence to stationarity. The approach is based on the realization of the transition semigroup associated with the solution of a stochastic differential equation as a strongly continuous semigroup in the Lp-space with respect to a weight that plays the role of a sub-stationary or stationary density. This way we obtain in particular a rigorous functional analytic description of the generator of the solution of a stochastic differential equation and its full domain. The existence of such a weight is shown under broad assumptions on the coefficients. A remarkable fact is that although the weight may not be unique, many important results are independent of it. Given such a weight and semigroup, one can construct and further analyze in detail a weak solution to the stochastic differential equation combining variational techniques, regularity theory for partial differential equations, potential, and generalized Dirichlet form theory. Under classical-like or various other criteria for non-explosion we obtain as one of our main applications the existence of a pathwise unique and strong solution with an infinite lifetime. These results substantially supplement the classical case of locally Lipschitz or monotone coefficients.We further treat other types of uniqueness and non-uniqueness questions, such as uniqueness and non-uniqueness of the mentioned weights and uniqueness in law, in a certain sense, of the solution.

An Illustrative Introduction to Modern Analysis

Author : Nikolaos Katzourakis
Publisher : CRC Press
ISBN 13 : 1351765329
Total Pages : 378 pages
Book Rating : 4.3/5 (517 download)

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Book Synopsis An Illustrative Introduction to Modern Analysis by : Nikolaos Katzourakis

Download or read book An Illustrative Introduction to Modern Analysis written by Nikolaos Katzourakis and published by CRC Press. This book was released on 2018-01-02 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.

The Steady Navier-Stokes System

Author : Mikhail Korobkov
Publisher : Springer Nature
ISBN 13 : 303150898X
Total Pages : 296 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis The Steady Navier-Stokes System by : Mikhail Korobkov

Download or read book The Steady Navier-Stokes System written by Mikhail Korobkov and published by Springer Nature. This book was released on with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Convex Functions and Their Applications

Author : Constantin P. Niculescu
Publisher : Springer
ISBN 13 : 3319783378
Total Pages : 415 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Convex Functions and Their Applications by : Constantin P. Niculescu

Download or read book Convex Functions and Their Applications written by Constantin P. Niculescu and published by Springer. This book was released on 2018-06-08 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thorough introduction to an important area of mathematics Contains recent results Includes many exercises

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

Author : N. V. Krylov
Publisher : American Mathematical Soc.
ISBN 13 : 1470447401
Total Pages : 441 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations by : N. V. Krylov

Download or read book Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations written by N. V. Krylov and published by American Mathematical Soc.. This book was released on 2018-09-07 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov–Safonov and the Evans–Krylov theorems, are taken from old sources, and the main results were obtained in the last few years. Presentation of these results is based on a generalization of the Fefferman–Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called “ersatz” existence theorems, saying that one can slightly modify “any” equation and get a “cut-off” equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.

An Introduction to Number Theory with Cryptography

Author : James Kraft
Publisher : CRC Press
ISBN 13 : 1315161001
Total Pages : 578 pages
Book Rating : 4.3/5 (151 download)

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Book Synopsis An Introduction to Number Theory with Cryptography by : James Kraft

Download or read book An Introduction to Number Theory with Cryptography written by James Kraft and published by CRC Press. This book was released on 2018-01-29 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum. Features of the second edition include Over 800 exercises, projects, and computer explorations Increased coverage of cryptography, including Vigenere, Stream, Transposition,and Block ciphers, along with RSA and discrete log-based systems "Check Your Understanding" questions for instant feedback to students New Appendices on "What is a proof?" and on Matrices Select basic (pre-RSA) cryptography now placed in an earlier chapter so that the topic can be covered right after the basic material on congruences Answers and hints for odd-numbered problems About the Authors: Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School. Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.

A Tour through Graph Theory

Author : Karin R Saoub
Publisher : CRC Press
ISBN 13 : 1351642952
Total Pages : 342 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis A Tour through Graph Theory by : Karin R Saoub

Download or read book A Tour through Graph Theory written by Karin R Saoub and published by CRC Press. This book was released on 2017-11-02 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Tour Through Graph Theory introduces graph theory to students who are not mathematics majors. Rather than featuring formal mathematical proofs, the book focuses on explanations and logical reasoning. It also includes thoughtful discussions of historical problems and modern questions. The book inspires readers to learn by working through examples, drawing graphs and exploring concepts. This book distinguishes itself from others covering the same topic. It strikes a balance of focusing on accessible problems for non-mathematical students while providing enough material for a semester-long course. Employs graph theory to teach mathematical reasoning Expressly written for non-mathematical students Promotes critical thinking and problem solving Provides rich examples and clear explanations without using proofs

Discovering Group Theory

Author : Tony Barnard
Publisher : CRC Press
ISBN 13 : 1315405768
Total Pages : 286 pages
Book Rating : 4.3/5 (154 download)

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Book Synopsis Discovering Group Theory by : Tony Barnard

Download or read book Discovering Group Theory written by Tony Barnard and published by CRC Press. This book was released on 2016-12-19 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.

Topics in Spectral Geometry

Author : Michael Levitin
Publisher : American Mathematical Society
ISBN 13 : 1470475251
Total Pages : 346 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topics in Spectral Geometry by : Michael Levitin

Download or read book Topics in Spectral Geometry written by Michael Levitin and published by American Mathematical Society. This book was released on 2023-11-30 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the geometry of the underlying object, e.g., a Euclidean domain or a Riemannian manifold, on which the operator is defined. This dependence, or, rather, the interplay between the geometry and the spectrum, is the main subject of spectral geometry. Its roots can be traced to Ernst Chladni's experiments with vibrating plates, Lord Rayleigh's theory of sound, and Mark Kac's celebrated question “Can one hear the shape of a drum?” In the second half of the twentieth century spectral geometry emerged as a separate branch of geometric analysis. Nowadays it is a rapidly developing area of mathematics, with close connections to other fields, such as differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. This book can be used for a graduate or an advanced undergraduate course on spectral geometry, starting from the basics but at the same time covering some of the exciting recent developments which can be explained without too many prerequisites.

Introduction to Number Theory

Author : Anthony Vazzana
Publisher : CRC Press
ISBN 13 : 1498717500
Total Pages : 426 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Introduction to Number Theory by : Anthony Vazzana

Download or read book Introduction to Number Theory written by Anthony Vazzana and published by CRC Press. This book was released on 2015-11-18 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbert's tenth problem.

Real Analysis and Foundations, Fourth Edition

Author : Steven G. Krantz
Publisher : CRC Press
ISBN 13 : 1498777708
Total Pages : 304 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Real Analysis and Foundations, Fourth Edition by : Steven G. Krantz

Download or read book Real Analysis and Foundations, Fourth Edition written by Steven G. Krantz and published by CRC Press. This book was released on 2016-12-12 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Readable yet Rigorous Approach to an Essential Part of Mathematical Thinking Back by popular demand, Real Analysis and Foundations, Third Edition bridges the gap between classic theoretical texts and less rigorous ones, providing a smooth transition from logic and proofs to real analysis. Along with the basic material, the text covers Riemann-Stieltjes integrals, Fourier analysis, metric spaces and applications, and differential equations. New to the Third Edition Offering a more streamlined presentation, this edition moves elementary number systems and set theory and logic to appendices and removes the material on wavelet theory, measure theory, differential forms, and the method of characteristics. It also adds a chapter on normed linear spaces and includes more examples and varying levels of exercises. Extensive Examples and Thorough Explanations Cultivate an In-Depth Understanding This best-selling book continues to give students a solid foundation in mathematical analysis and its applications. It prepares them for further exploration of measure theory, functional analysis, harmonic analysis, and beyond.