Absolute Measurable Spaces (Encyclopedia of Mathematics and by Togo Nishiura

By Togo Nishiura

Absolute measurable house and absolute null house are very previous topological notions, constructed from famous evidence of descriptive set idea, topology, Borel degree conception and research. This monograph systematically develops and returns to the topological and geometrical origins of those notions. Motivating the advance of the exposition are the motion of the crowd of homeomorphisms of an area on Borel measures, the Oxtoby-Ulam theorem on Lebesgue-like measures at the unit dice, and the extensions of this theorem to many different topological areas. lifestyles of uncountable absolute null area, extension of the Purves theorem and up to date advances on homeomorphic Borel chance measures at the Cantor house, are one of the issues mentioned. A short dialogue of set-theoretic effects on absolute null area is given, and a four-part appendix aids the reader with topological measurement concept, Hausdorff degree and Hausdorff measurement, and geometric degree theory.

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