Absolute measurable spaces
著者
書誌事項
Absolute measurable spaces
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 120）
Cambridge University Press, 2008
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注記
Bibliography: p. [258]-265
Includes indexes
内容説明・目次
内容説明
Absolute measurable space and absolute null space are very old topological notions, developed from well-known facts of descriptive set theory, topology, Borel measure theory and analysis. This monograph systematically develops and returns to the topological and geometrical origins of these notions. Motivating the development of the exposition are the action of the group of homeomorphisms of a space on Borel measures, the Oxtoby-Ulam theorem on Lebesgue-like measures on the unit cube, and the extensions of this theorem to many other topological spaces. Existence of uncountable absolute null space, extension of the Purves theorem and recent advances on homeomorphic Borel probability measures on the Cantor space, are among the many topics discussed. A brief discussion of set-theoretic results on absolute null space is given, and a four-part appendix aids the reader with topological dimension theory, Hausdorff measure and Hausdorff dimension, and geometric measure theory.
目次
- Preface
- 1. The absolute property
- 2. The universally measurable property
- 3. The Homeomorphism Group of X
- 4. Real-valued functions
- 5. Hausdorff measure and dimension
- 6. Martin axiom
- Appendix A. Preliminary material
- Appendix B. Probability theoretic approach
- Appendix C. Cantor spaces
- Appendix D. Dimensions and measures
- Bibliography.
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