Set theoretical aspects of real analysis / Alexander B. Kharazishvili, Tbilisi State University, Georgia.

Format:

Book

Author/Creator:

Kharazishvili, A. B., author.

Series:

Monographs and research notes in mathematics.

Monographs and Research Notes in Mathematics

Language:

English

Subjects (All):

Mathematical analysis.

Set theory.

Physical Description:

1 online resource (452 p.)

Edition:

1st ed.

Place of Publication:

Boca Raton : CRC Press, [2015]

Language Note:

English

Summary:

<P>This book addresses a number of questions in real analysis and classical measure theory that are of a set-theoretic flavor. Accessible to graduate students, the beginning of the book presents introductory topics on real analysis and Lebesque measure theory. These topics highlight the boundary between fundamental concepts of measurability and non-measurability for point sets and functions. The remainder of the book deals with more specialized material on set-theoretical real analysis. Problems are included at the end of each chapter.</P>

Contents:

Front Cover; Table of Contents; Preface; Chapter 1: ZF Theory and Some Point Sets on the Real Line; Chapter 2: Countable Versions of AC and Real Analysis; Chapter 3: Uncountable Versions of AC and Lebesgue Nonmeasurable Sets; Chapter 4: The Continuum Hypothesis and Lebesgue Nonmeasurable Sets; Chapter 5: Measurability Properties of Sets and Functions; Chapter 6: Radon Measures and Nonmeasurable Sets; Chapter 7: Real-Valued Step Functions with Strange Measurability Properties; Chapter 7: A Partition of the Real Line Into Continuum Many Thick Subsets

Chapter 9: Measurability Properties of Vitali SetsChapter 10: A Relationship Between the Measurability and Continuity of Real-Valued Functions; Chapter 11: A Relationship Between Absolutely Nonmeasurable Functions and Sierpiński-Zygmund Type Functions; Chapter 12: Sums of Absolutely Nonmeasurable Injective Functions; Chapter 13: A Large Group of Absolutely Nonmeasurable Additive Functions; Chapter 14: Additive Properties of Certain Classes of Pathological Functions; Chapter 15: Absolutely Nonmeasurable Homomorphisms of Commutative Groups

Chapter 16: Measurable and Nonmeasurable Sets With Homogeneous SectionsChapter 17: A Combinatorial Problem on Translation Invariant Extensions of the Lebesgue Measure; Chapter 18: Countable Almost Invariant Partitions of G-Spaces; Chapter 19: Nonmeasurable Unions of Measure Zero Sections of Plane Sets; Chapter 20: Measurability Properties of Well-Orderings; Appendix 1: The Axioms of Set Theory; Appendix 2: The Axiom of Choice and Generalized Continuum Hypothesis; Appendix 3: Martin's Axiom and its consequences in real analysis; Appendix 4: ω1-dense subsets of the real line

Appendix 5: The Beginnings of Descriptive Set TheoryBibliography; Back Cover

Notes:

A Chapman and Hall book.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-429-17057-2

1-4822-4201-X

9780429170577

OCLC:

890721085