Set theoretical aspects of real analysis
By: Alexander B. Kharazishvili, Tbilisi State University, Georgia
Series: Monographs and research notes in mathematics
Publisher: CRC Press, Taylor & Francis Group
Published: 2015
Place of publication: Boca Raton
Language: eng
Number of pages: 433
ISBN-13: 9781482242010
Copyright date: 2015
Subjects: Mathematical analysis; Set theory
Notes: "A Chapman & Hall book."

Includes bibliographical references (pages 411-428) and index.
Table of contents: title: 1.; title: ZF theory and some point sets on the real line -- -- 2.; title: Countable versions of AC and real analysis -- -- 3.; title: Uncountable versions of AC and Lebesgue nonmeasurable sets -- -- 4.; title: The Continuum Hypothesis and Lebesgue nonmeasurable sets -- -- 5.; title: Measurability properties of sets and functions -- -- 6.; title: Radon measures and nonmeasurable sets -- -- 7.; title: Real-valued step functions with strange measurability properties -- -- 8.; title: A partition of the real line into continuum many thick subsets -- -- 9.; title: Measurability properties of Vitali sets -- -- 10.; title: A relationship between the measurability and continuity of real-valued functions -- -- 11.; title: A relationship between absolutely nonmeasurable functions and Sierpiński-Zygmund type functions -- -- 12.; title: Sums of absolutely nonmeasurable injective functions -- -- 13.; title: A large group of absolutely nonmeasurable additive functions -- -- 14.; title: Additive properties of certain classes of pathological functions -- -- 15.; title: Absolutely nonmeasurable homomorphisms of commutative groups -- -- 16.; title: Measurable and nonmeasurable sets with homogeneous sections -- -- 17.; title: A combinatorial problem on translation invariant extensions of the Lebesgue measure -- -- 18.; title: Countable almost invariant partitions of G-spaces -- -- 19.; title: Nonmeasurable unions of measure zero sections of plane sets -- -- 20.; title: Measurability properties of well-orderings.