Notes on real analysis and measure theory : fine properties of real sets and functions / Alexander Kharazishvili.
Kharazishvili, A. B., author.
2022
QA331.5
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Title Notes on real analysis and measure theory : fine properties of real sets and functions / Alexander Kharazishvili.
Author Kharazishvili, A. B., author.
ISBN 9783031170331 (electronic bk.)
3031170334 (electronic bk.)
9783031170324
DOI https://doi.org/10.1007/978-3-031-17033-1
Published Cham : Springer, [2022]
Copyright ©2022
Language English
Description 1 online resource (xi, 253 pages).
Other Standard Identifiers 10.1007/978-3-031-17033-1 doi
Call Number QA331.5
Dewey Decimal Classification 515/.8
Summary This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed September 28, 2022).
Series Springer monographs in mathematics. 2196-9922
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Preface
1. Real-Valued Semicontinuous Functions
2. The Oscillations of Real-Valued Functions
3. Monotone and Continuous Restrictions of Real-Valued Functions
4. Bijective Continuous Images of Absolute Null Sets
5. Projective Absolutely Nonmeasurable Functions
6. Borel Isomorphisms of Analytic Sets
7. Iterated Integrals of Real-Valued Functions of Two Real Variables
8. The Steinhaus Property, Ergocidity, and Density Points
9. Measurability Properties of H-Selectors and Partial H-Selectors
10. A Decomposition of an Uncountable Solvable Group into Three Negligible Sets
11. Negligible Sets Versus Absolutely Nonmeasurable Sets
12. Measurability Properties of Mazurkiewicz Sets
13. Extensions of Invariant Measures on R
A. A Characterization of Uncountable Sets in Terms of their Self-Mappings
B. Some Applications of Peano Type Functions
C. Almost Rigid Mathematical Structures
D. Some Unsolved Problems in Measure Theory
Bibliography
Index.

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