Set theoretical aspects of real analysis /

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 betwee...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Kharazishvili, A. B. (Author)
Format: Electronic eBook
Language:Inglés
Published: Boca Raton : CRC Press/Taylor and Francis, [2014]
Series:Monographs and research notes in mathematics.
Subjects:
Set theory.
Measure theory.
Théorie des ensembles.
Théorie de la mesure.
MATHEMATICS > Topology.
Measure theory
Set theory
Online Access:Texto completo
Table of 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.
  • Appendix 5: The Beginnings of Descriptive Set TheoryBibliography; Back Cover.

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