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Author : D. H. Fremlin
Publisher :
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4.3/5 (121 download)
Download or read book Measure-additive Coverings and Measurable Selectors written by D. H. Fremlin and published by . This book was released on 1987 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. Daniel Mauldin
Publisher : American Mathematical Soc.
ISBN 13 : 0821850997
Total Pages : 352 pages
Book Rating : 4.8/5 (218 download)
Download or read book Measure and Measurable Dynamics written by R. Daniel Mauldin and published by American Mathematical Soc.. This book was released on 1989 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dorothy Maharam Stone's contributions to operators and measure algebras has had a profound influence on this area of research. This volume contains the proceedings of the Conference on Measure and Measurable Dynamics, held in honor of Stone at the University of Rochester in September 1987.
Author : D. H. Fremlin
Publisher : Torres Fremlin
ISBN 13 : 0953812960
Total Pages : 375 pages
Book Rating : 4.9/5 (538 download)
Download or read book Measure Theory written by D. H. Fremlin and published by Torres Fremlin. This book was released on 2000 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Beloslav Riecan
Publisher : Springer Science & Business Media
ISBN 13 : 9401589194
Total Pages : 389 pages
Book Rating : 4.4/5 (15 download)
Download or read book Integral, Measure, and Ordering written by Beloslav Riecan and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is a monograph including some recent results of mea sure and integration theory. It concerns three main ideas. The first idea deals with some ordering structures such as Riesz spaces and lattice or dered groups, and their relation to measure and integration theory. The second is the idea of fuzzy sets, quite new in general, and in measure theory particularly. The third area concerns some models of quantum mechanical systems. We study mainly models based on fuzzy set theory. Some recent results are systematically presented along with our suggestions for further development. The first chapter has an introductory character, where we present basic definitions and notations. Simultaneously, this chapter can be regarded as an elementary introduction to fuzzy set theory. Chapter 2 contains an original approach to the convergence of sequences of measurable functions. While the notion of a null set can be determined uniquely, the notion of a set of "small" measure has a fuzzy character. It is interesting that the notion of fuzzy set and the notion of a set of small measure (described mathematically by so-called small systems) were introduced independently at almost the same time. Although the axiomatic systems in both theories mentioned are quite different, we show that the notion of a small system can be considered from the point of view of fuzzy sets.
Author : Alexander Kharazishvili
Publisher : CRC Press
ISBN 13 : 1351650513
Total Pages : 376 pages
Book Rating : 4.3/5 (516 download)
Download or read book Strange Functions in Real Analysis written by Alexander Kharazishvili and published by CRC Press. This book was released on 2017-10-16 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strange Functions in Real Analysis, Third Edition differs from the previous editions in that it includes five new chapters as well as two appendices. More importantly, the entire text has been revised and contains more detailed explanations of the presented material. In doing so, the book explores a number of important examples and constructions of pathological functions. After introducing basic concepts, the author begins with Cantor and Peano-type functions, then moves effortlessly to functions whose constructions require what is essentially non-effective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, the author considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms. On the whole, the book is devoted to strange functions (and point sets) in real analysis and their applications.
Author : Alexander B. Kharazishvili
Publisher : CRC Press
ISBN 13 : 148224201X
Total Pages : 457 pages
Book Rating : 4.4/5 (822 download)
Download or read book Set Theoretical Aspects of Real Analysis written by Alexander B. Kharazishvili and published by CRC Press. This book was released on 2014-08-26 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary between fundamental concepts of measurability and nonmeasurability for point sets and functions. The remainder of the book deals with more specialized material on set theoretical real analysis. The book focuses on certain logical and set theoretical aspects of real analysis. It is expected that the first eleven chapters can be used in a course on Lebesque measure theory that highlights the fundamental concepts of measurability and non-measurability for point sets and functions. Provided in the book are problems of varying difficulty that range from simple observations to advanced results. Relatively difficult exercises are marked by asterisks and hints are included with additional explanation. Five appendices are included to supply additional background information that can be read alongside, before, or after the chapters. Dealing with classical concepts, the book highlights material not often found in analysis courses. It lays out, in a logical, systematic manner, the foundations of set theory providing a readable treatment accessible to graduate students and researchers.
Author : Vladimir I. Bogachev
Publisher : Springer Science & Business Media
ISBN 13 : 3540345140
Total Pages : 1075 pages
Book Rating : 4.5/5 (43 download)
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.
Author : Lev Bukovský
Publisher : Springer Science & Business Media
ISBN 13 : 3034800061
Total Pages : 546 pages
Book Rating : 4.0/5 (348 download)
Download or read book The Structure of the Real Line written by Lev Bukovský and published by Springer Science & Business Media. This book was released on 2011-03-02 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapid development of set theory in the last fifty years, mainly by obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the real line and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, and descriptive set theory are revisited with the purpose of eliminating superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statements pertaining to properties of the real line are shown to be undecidable in set theory. The metamathematics behind set theory is shortly explained in the appendix. Each section contains a series of exercises with additional results.
Author : A.B. Kharazishvili
Publisher : Springer Science & Business Media
ISBN 13 : 9401707502
Total Pages : 248 pages
Book Rating : 4.4/5 (17 download)
Download or read book Applications of Point Set Theory in Real Analysis written by A.B. Kharazishvili and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to some results from the classical Point Set Theory and their applications to certain problems in mathematical analysis of the real line. Notice that various topics from this theory are presented in several books and surveys. From among the most important works devoted to Point Set Theory, let us first of all mention the excellent book by Oxtoby [83] in which a deep analogy between measure and category is discussed in detail. Further, an interesting general approach to problems concerning measure and category is developed in the well-known monograph by Morgan [79] where a fundamental concept of a category base is introduced and investigated. We also wish to mention that the monograph by Cichon, W«;glorz and the author [19] has recently been published. In that book, certain classes of subsets of the real line are studied and various cardinal valued functions (characteristics) closely connected with those classes are investigated. Obviously, the IT-ideal of all Lebesgue measure zero subsets of the real line and the IT-ideal of all first category subsets of the same line are extensively studied in [19], and several relatively new results concerning this topic are presented. Finally, it is reasonable to notice here that some special sets of points, the so-called singular spaces, are considered in the classi
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1988-03 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : M. Husek
Publisher : Elsevier
ISBN 13 : 0080934439
Total Pages : 808 pages
Book Rating : 4.0/5 (89 download)
Download or read book Recent Progress in General Topology written by M. Husek and published by Elsevier. This book was released on 1992-11-20 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan, North-Holland, 1984), which gives an almost complete picture of the state of the art of Set Theoretic Topology before 1984. In the present volume several important developments are surveyed that surfaced in the period 1984-1991. This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990). Solutions to some of the original 1100 open problems are discussed and new problems are posed.
Author : A.B. Kharazishvili
Publisher : CRC Press
ISBN 13 : 9780824703202
Total Pages : 320 pages
Book Rating : 4.7/5 (32 download)
Download or read book Strange Functions in Real Analysis, Second Edition written by A.B. Kharazishvili and published by CRC Press. This book was released on 2000-01-31 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to explicate extraordinary functions in real analysis and their applications. It examines the Baire category method, the Zermelo-Fraenkel set, the Axiom of Dependent Choices, Cantor and Peano type functions, the Continuum Hypothesis, everywhere differentiable nowhere monotone functions, and Jarnik's nowhere approximately differentiable functions.
Author : David W. Jones
Publisher :
ISBN 13 :
Total Pages : 122 pages
Book Rating : 4.3/5 (121 download)
Download or read book A General Theory of Polyhedral Sets and the Corresponding T-complexes written by David W. Jones and published by . This book was released on 1988 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bogdan Ziemian
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.3/5 (121 download)
Download or read book Taylor Formula for Distributions written by Bogdan Ziemian and published by . This book was released on 1988 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : N. Ashley
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.3/5 (121 download)
Download or read book Simplicial T-complexes and Crossed Complexes written by N. Ashley and published by . This book was released on 1988 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andrzej Piątkowski
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.3/5 (121 download)
Download or read book A Stability Theorem for Foliations with Singularities written by Andrzej Piątkowski and published by . This book was released on 1988 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. C. Mayer
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.3/5 (121 download)
Download or read book Containing Spaces for Planar Rational Compacta written by J. C. Mayer and published by . This book was released on 1990 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
