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Notes on Real Analysis and Measure Theory = Fine Properties of Real Sets and Functions /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Notes on Real Analysis and Measure Theory/ by Alexander Kharazishvili.
Reminder of title:	Fine Properties of Real Sets and Functions /
Author:	Kharazishvili, Alexander.
Description:	XI, 253 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematics. -
Online resource:	https://doi.org/10.1007/978-3-031-17033-1
ISBN:	9783031170331

Notes on Real Analysis and Measure Theory = Fine Properties of Real Sets and Functions /
Kharazishvili, Alexander.

Notes on Real Analysis and Measure TheoryFine Properties of Real Sets and Functions /[electronic resource] :by Alexander Kharazishvili. - 1st ed. 2022. - XI, 253 p.online resource. - Springer Monographs in Mathematics,2196-9922. - Springer Monographs in Mathematics,.

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.

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.

ISBN: 9783031170331

Standard No.: 10.1007/978-3-031-17033-1doiSubjects--Topical Terms:

527692
Mathematics.

LC Class. No.: QA1-939

Dewey Class. No.: 510

Notes on Real Analysis and Measure Theory = Fine Properties of Real Sets and Functions /
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