Absolute Measurable Spaces

by Togo Nishiura

Overview

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.

Product Details

ISBN-13:	9780521875561
Publisher:	Cambridge University Press
Publication date:	05/08/2008
Series:	Encyclopedia of Mathematics and its Applications , #120
Pages:	292
Product dimensions:	6.30(w) x 9.45(h) x 0.79(d)

About the Author

Togo Nishiura is Professor Emeritus at Wayne State University, Detroit and Associate Fellow in Mathematics at Dickinson College, Pennsylvania.

Table of Contents

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.

Editorial Reviews

"The monograph nicely connects classical ideas and examples with newer investigations. The book should be very useful for a wide audience of graduate students and researchers. Starting from basic considerations the reader is gently led to more advanced results and methods. Thanks to an in-depth treatment of the subject, several concepts are thoroughly developed."
Marek Balcerzak, Mathematical Reviews

From the Publisher