Notes on real analysis and measure theory : fine properties of real sets and functions / Alexander Kharazishvili.

Format:

Book

Author/Creator:

Kharazishvili, A. B., author.

Series:

Springer monographs in mathematics 1439-7382

Springer monographs in mathematics, 1439-7382

Language:

English

Subjects (All):

Measure theory.

Set theory.

Mathematical analysis.

Functions of real variables.

Physical Description:

xi, 253 pages ; 24 cm.

Place of Publication:

Cham : Springer, [2022]

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"--Back cover.

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.

Notes:

Includes bibliographical references and index.

ISBN:

9783031170324

3031170326

OCLC:

1342248442