Applications of Point Set Theory in Real Analysis
By: by A. B. Kharazishvili
Series: Mathematics and Its Applications -- 429; Mathematics and Its Applications -- 429
Publisher: Springer Netherlands
Published: 1998
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 240
ISBN-13: 9789048150069; 9789401707503
Subjects: Harmonic analysis; Mathematics; Symbolic and mathematical Logic; Topology
Description: 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. Audience: The material presented in the book is essentially self-contained and is accessible to a wide audience of mathematicians. It will appeal to specialists in set theory, mathematical analysis, measure theory and general topology. It can also be recommended as a textbook for postgraduate students who are interested in the applications of set-theoretical methods to the above-mentioned domains of mathematics.
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