Uniformly σ-Finite Disintegrations of Measures

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.

Creator(s): Backs, Karl
Creation Date: August 2011
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
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Publisher Info:
Publisher Name: University of North Texas
Publisher Info: Web: www.unt.edu
Place of Publication: Denton, Texas
Date(s):
  • Creation: August 2011
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.

Degree:
Discipline: Mathematics
Level: Doctoral
PublicationType: Doctoral Dissertation
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Subject(s):
Keyword(s): Measure theory | uniformization | analysis | disintegration of measure
Contributor(s):
Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • LOCAL-CONT-NO: backs_karl
  • ARK: ark:/67531/metadc84165
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Public
Holder: Backs, Karl
License: Copyright
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.