Applications of Point Set Theory in Real Analysis: 429 (Mathematics and Its Applications, 429) - Hardcover

Kharazishvili, A.B.

Hardcover

ISBN 10: 0792349792 ISBN 13: 9780792349792

Publisher: Springer, 1998

Synopsis

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

About this title

Review

.....`It is also recommended as a textbook for postgraduate students.'
European Mathematical Society News, December 1999

Synopsis

The main goal of this book is to demonstrate the usefulness of set-theoretical methods in various questions of real analysis and classical measure theory. In this context, many statements and facts from analysis are treated as consequences of purely set-theoretical assertions which can successfully be applied to measures and Baire category. Topics covered include similarities and differences between measure and category; constructions of nonmeasurable sets and of sets without the Baire property; three aspects of the measure extension problem; the principle of condensation of singularities from the point of view of the Kuratowski-Ulam theorem; transformation groups and invariant (quasi-invariant) measures; the uniqueness property of an invariant measure; and ordinary differential equations with nonmeasurable right-hand sides. The material presented in the book is essentially self-contained and should be accessible to a wide audience of mathematicians. It may appeal to specialists in set theory, mathematical analysis, measure theory and general topology.

It can also be used as a textbook for postgraduate students who are interested in the applications of set-theoretical methods to the above-mentioned domains of mathematics.

Edition details

• Publisher: Springer
• Publication date: 1998
• Language: English
• ISBN 10: 0792349792
• ISBN 13: 9780792349792
• Binding: Hardcover
• Number of pages: 248