Absolute Measurable Spaces

Erscheinungsjahr 2010
ISBN: 978-0-521-87556-1
Verlag: Cambridge University Press

Buch, Englisch, Band 120, 288 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 605 g

Reihe: Encyclopedia of Mathematics and its Applications

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.

Autoren/Hrsg.

Nishiura, Togo

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie

Inhaltsverzeichnis

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.

Über Autor(innen)

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