Uniformly σ-Finite Disintegrations of Measures

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A disintegration of measure is a common tool used in ergodic theory, probability, and descriptive set theory. The primary interest in this paper is in disintegrating σ-finite measures on standard Borel spaces into families of σ-finite measures. In 1984, Dorothy Maharam asked whether every such disintegration is uniformly σ-finite meaning that there exists a countable collection of Borel sets which simultaneously witnesses that every measure in the disintegration is σ-finite. Assuming Gödel’s axiom of constructability I provide answer Maharam's question by constructing a specific disintegration which is not uniformly σ-finite.

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Backs, Karl August 2011.

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  • Backs, Karl

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Description

A disintegration of measure is a common tool used in ergodic theory, probability, and descriptive set theory. The primary interest in this paper is in disintegrating σ-finite measures on standard Borel spaces into families of σ-finite measures. In 1984, Dorothy Maharam asked whether every such disintegration is uniformly σ-finite meaning that there exists a countable collection of Borel sets which simultaneously witnesses that every measure in the disintegration is σ-finite. Assuming Gödel’s axiom of constructability I provide answer Maharam's question by constructing a specific disintegration which is not uniformly σ-finite.

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  • August 2011

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  • May 17, 2012, 9:47 p.m.

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  • June 26, 2012, 10:40 a.m.

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Backs, Karl. Uniformly σ-Finite Disintegrations of Measures, dissertation, August 2011; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc84165/: accessed April 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .