Absolute Measurable Spaces

Front Cover
Cambridge University Press, May 8, 2008 - Mathematics - 274 pages
0 Reviews
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Section 1
4
Section 2
30
Section 3
35
Section 4
53
Section 5
70
Section 6
73
Section 7
77
Section 8
91
Section 9
97
Section 10
99
Section 11
104
Section 12
123
Section 13
135
Section 14
136
Section 15
157

Common terms and phrases

About the author (2008)

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

Bibliographic information