Set theoretical aspects of real analysis - Kharazishvili, A. B., author (Boca Raton CRC Press, Taylor & Francis Group, 2015)
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.
Includes bibliographical references (pages 411-428) and index.
Keywords: Mathematical analysis; Set theory