TY - BOOK ID - 66956871 TI - Absolute measurable spaces PY - 2008 VL - 120 SN - 9780521875561 0521875560 9780511721380 9781461941545 1461941547 0511721382 9781107390492 1107390494 1139883402 1107384060 1107387574 0511839758 1107398908 1107395291 PB - Cambridge : Cambridge University Press, DB - UniCat KW - Topological spaces. KW - Spaces, Topological UR - https://www.unicat.be/uniCat?func=search&query=sysid:66956871 AB - 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. ER -