Nonmeasurable sets and functions /

The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Kharazishvili, A. B.
Format: Electronic eBook
Language:Inglés
Published: Amsterdam ; Boston : Elsevier, 2004.
Edition:1st ed.
Series:North-Holland mathematics studies ; 195.
Subjects:
Measure theory.
Functional analysis.
Set theory.
Th�eorie de la mesure.
Analyse fonctionnelle.
Th�eorie des ensembles.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Functional analysis
Measure theory
Set theory
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Table of Contents:
  • 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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