Uniformly σ-Finite Disintegrations of Measures

• Main Author: Backs, Karl
• Other Authors: Mauldin, R. Daniel
• Format: Others
• Language: English
• Published: University of North Texas 2011
• Subjects: Measure theory; uniformization; analysis; disintegration of measure
• Online Access: https://digital.library.unt.edu/ark:/67531/metadc84165/

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.