Absolute Measurable Spaces

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.

Author: Togo Nishiura
Publisher: Cambridge University Press
Published: 05/08/2008
Pages: 292
Binding Type: Hardcover
Weight: 1.36lbs
Size: 9.21h x 6.48w x 0.82d
ISBN: 9780521875561

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

This title is not returnable