Applications of Point Set Theory in Real Analysis

Preface. 0. Introduction: Preliminary Facts. 1. Set-Valued Mappings. 2. Nonmeasurable Sets and Sets without the Baire Property. 3. Three Aspects of the Measure Extension Problem. 4. Some Properties of sigma-algebras and sigma-ideals. 5. Nonmeasurable Subgroups of the Real Line. 6. Additive Properties of Invariant sigma-Ideals on the Real Line. 7. Translations of Sets and Functions. 8. The Steinhaus Property of Invariant Measures. 9. Some Applications of the Property (N of Luzin. 10. The Principle of Condensation of Singularities. 11. The Uniqueness of Lebesgue and Borel Measures. 12. Some Subsets of Spaces Equipped with Transformation Groups. 13. Sierpinski's Partition and Its Applications. 14. Selectors Associated with Subgroups of the Real Line. 15. Set Theory and Ordinary Differential Equations. Bibliography. Subject Index.