Nonmeasurable Sets and Functions - 1st Edition - ISBN: 9780444516268, 9780080479767

Nonmeasurable Sets and Functions, Volume 195

1st Edition

Authors: Alexander Kharazishvili
Hardcover ISBN: 9780444516268
eBook ISBN: 9780080479767
Imprint: Elsevier Science
Published Date: 29th May 2004
Page Count: 349
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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.


Description

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.

Key Features

· highlights the importance of nonmeasurable sets (functions) for general measure extension problem. · Deep connections of the topic with set theory, real analysis, infinite combinatorics, group theory and geometry of Euclidean spaces shown and underlined. · self-contained and accessible for a wide audience of potential readers. · Each chapter ends with exercises which provide valuable additional information about nonmeasurable sets and functions. · Numerous open problems and questions.

Readership

Pure mathematicians and post-graduate students. Especially, those ones whose research interests lie in set theory, real analysis, measure theory, general topology , geometry of Euclidean spaces, group theory.


Details

No. of pages:
349
Language:
English
Copyright:
© Elsevier Science 2004
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080479767
Hardcover ISBN:
9780444516268

Reviews

"The author has done a very good job writing a useful book on a theme which had not previously been described so thoroughly in the literature." Marek Balcerak (Lódz, Poland) in: Mathematical Reviews (2005d: 28001)


About the Authors

Alexander Kharazishvili Author

Affiliations and Expertise

Tbilisi State University, Tbilisi, Republic of Georgia.