Overview

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.

Full Product Details

Author:   A.B. Kharazishvili
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 1998
Volume:   429
Dimensions:   Width: 15.50cm , Height: 1.30cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9789048150069

ISBN 10:   904815006
Pages:   240
Publication Date:   06 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

0. Introduction: preliminary facts.- 1. Set-valued mappings.- 2. Nonmeasurable sets and sets without the Baire property.- 3. Three aspects of the measure extension problem.- 4. Some properties of ?-algebras and ?-ideals.- 5. Nonmeasurable subgroups of the real line.- 6. Additive properties of invariant ?-ideals on the real line.- 7. Translations of sets and functions.- 8. The Steinhaus property of invariant measures.- 9. Some applications of the property (N) of Luzin.- 10. The principle of condensation of singularities.- 11. The uniqueness of Lebesgue and Borel measures.- 12. Some subsets of spaces equipped with transformation groups.- 13. Sierpi?ski’s partition and its applications.- 14. Selectors associated with subgroups of the real line.- 15. Set theory and ordinary differential equations.

Reviews

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

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

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

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