Abstract
Contents Preface. 1. The Vitali theorem. 2. The Bernstein construction. 3. Nonmeasurable sets associated with Hamel bases. 4. The Fubini theorem and nonmeasurable sets. 5. Small nonmeasurable sets. 6. Strange subsets of the Euclidean plane. 7. Some special constructions of nonmeasurable sets. 8. The Generalized Vitali construction. 9. Selectors associated with countable subgroups. 10. Selectors associated with uncountable subgroups. 11. Absolutely nonmeasurable sets in groups. 12. Ideals producing nonmeasurable unions of sets. 13. Measurability properties of subgroups of a given group. 14. Groups of rotations and nonmeasurable sets. 15. Nonmeasurable sets associated with filters. Appendix 1: Logical aspects of the existence of nonmeasurable sets. Appendix 2: Some facts from the theory of commutative groups.
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