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Notes on Real Analysis and Measure Theory Fine Properties of Real Sets and Functions
Title
Notes on Real Analysis and Measure Theory [electronic resource] : Fine Properties of Real Sets and Functions / by Alexander Kharazishvili.
ISBN
9783031170331
Edition
1st ed. 2022.
Publication
Cham : Springer International Publishing : Imprint: Springer, 2022.
Physical Description
1 online resource (XI, 253 p.)
Local Notes
Access is available to the Yale community.
Access and use
Access restricted by licensing agreement.
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.
Variant and related titles
Springer ENIN.
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Format
Books / Online
Language
English
Added to Catalog
July 26, 2023
Series
Springer Monographs in Mathematics,
Contents
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.
Subjects
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