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Absolute Measurable Spaces Encyclopedia of Mathematics and its Applications 120 1st Edition by Togo Nishiura 0521875560 9780521875561

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Absolute Measurable Spaces Encyclopedia of Mathematics and its Applications 1st Edition Nishiura Togo Digital Instant Download

Author(s): Nishiura Togo
ISBN(s): 9780521875561, 0521875560
Edition: 1
File Details: PDF, 1.32 MB
Year: 2008
Language: english
SKU: EB-1381292 Category: Tag:

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Product details:

ISBN 10: 0521875560

ISBN 13: 9780521875561

Author: Togo Nishiura

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.

Absolute Measurable Spaces Encyclopedia of Mathematics and its Applications 120 1st Table of contents:

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

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