Applications of Point Set Theory in Real Analysis /
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...
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht :
Springer Netherlands,
1998.
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| Series: | Mathematics and its applications ;
429. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (viii, 240 pages) |
| ISBN: | 9789401707503 (electronic bk.) 9401707502 (electronic bk.) |