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....

Ausführliche Beschreibung

Bibliographische Detailangaben

1. Verfasser:	Nishiura, Togo 1931- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cambridge Cambridge University Press 2008
Schriftenreihe:	Encyclopedia of mathematics and its applications volume 120
Schlagworte:	Topological spaces Sigma-Algebra Hausdorff-Maß Maßraum Topologie
Online-Zugang:	BSB01 FHN01 Volltext
Zusammenfassung:	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
Beschreibung:	Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Beschreibung:	1 online resource (xii, 274 pages)
ISBN:	9780511721380
DOI:	10.1017/CBO9780511721380