By Togo Nishiura

Absolute measurable area and absolute null house are very outdated topological notions, constructed from famous proof of descriptive set thought, topology, Borel degree idea and research. This monograph systematically develops and returns to the topological and geometrical origins of those notions. Motivating the improvement 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 house, extension of the Purves theorem and up to date advances on homeomorphic Borel likelihood measures at the Cantor area, are one of many subject matters mentioned. A short dialogue of set-theoretic effects on absolute null area is given, and a four-part appendix aids the reader with topological size conception, Hausdorff degree and Hausdorff size, and geometric degree theory.

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