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

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Bibliographic Details
Main Author: Kharazishvili, A. B.
Language:English
Published: Boca Raton : CRC Press, Taylor & Francis Group, [2015]
Series:Monographs and research notes in mathematics.
Subjects:
Mathematical analysis.
Set theory.
Reelle Analysis.
Mengenlehre.
Online Access:
(Digital Object Identifier Permalink)
Physical Description:xxii, 433 pages ; 24 cm.
Format: Book
Contents:
  • 1. ZF theory and some point sets on the real line
  • 2. Countable versions of AC and real analysis
  • 3. Uncountable versions of AC and Lebesgue nonmeasurable sets
  • 4. The Continuum Hypothesis and Lebesgue nonmeasurable sets
  • 5. Measurability properties of sets and functions
  • 6. Radon measures and nonmeasurable sets
  • 7. Real-valued step functions with strange measurability properties
  • 8. A partition of the real line into continuum many thick subsets
  • 9. Measurability properties of Vitali sets
  • 10. A relationship between the measurability and continuity of real-valued functions
  • 11. A relationship between absolutely nonmeasurable functions and Sierpiński-Zygmund type functions
  • 12. Sums of absolutely nonmeasurable injective functions
  • 13. A large group of absolutely nonmeasurable additive functions
  • 14. Additive properties of certain classes of pathological functions
  • 15. Absolutely nonmeasurable homomorphisms of commutative groups
  • 16. Measurable and nonmeasurable sets with homogeneous sections
  • 17. A combinatorial problem on translation invariant extensions of the Lebesgue measure
  • 18. Countable almost invariant partitions of G-spaces
  • 19. Nonmeasurable unions of measure zero sections of plane sets
  • 20. Measurability properties of well-orderings.