Absolute Measurable Spaces (Encyclopedia of Mathematics and its Applications, Series Number 120) - Hardcover

Nishiura, Togo

Hardcover

ISBN 10: 0521875560 ISBN 13: 9780521875561

Publisher: Cambridge University Press, 2008

Synopsis

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.

About this title

Book Description

This monograph systematically develops and returns to the topological and geometrical origins of absolute measurable space. The existence of uncountable absolute null space and extension of the Purves theorem are among the many topics discussed. The exposition will suit researchers and graduate students of real analysis, set theory and measure theory.

About the Author

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

Edition details

• Publisher: Cambridge University Press
• Publication date: 2008
• ISBN 10: 0521875560
• ISBN 13: 9780521875561
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 292