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