Abstract
dc:description.abstractLet E be an analytic metric space, let X be a separable metric space with a regular Borel probability measure μ and let Π: E → X be a continuous map with μ(X \ Π(E)) =0. Schwartz’s lemma states that there exists a Borel cross-section for Π defined almost everywhere (μ). The equivalence classes of these Borel cross-sections are in one-to-one correspondence with the representations of the form Γ:C<sub>b</sub>(E) → L<sup>∞</sup>(μ) with Γ(f∘Π) = f for every f ∈ C<sub>b</sub>(X). The representations are also in one-to-one correspondence with equivalence classes of the minimal measures on E. Now let E, X, and μ be as above and let Π: E → X be an onto Borel map. There exists a Borel cross-section for Π defined almost everywhere (μ). The equivalence classes of the Borel cross-sections for Π are in one-to-one correspondence with the representations of the form Γ:B(E) → L<sup>∞</sup>(μ) with Γ(f∘Π) = f for every f in C<sub>b</sub>(X), where B(E) is the C*-algebra of the bounded Borel functions on E. The representations are also in one-to-one correspondence with equivalence classes of the minimal measures on E.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 1993
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Miller, Janice E.
- Chair dc:contributor.committeechair
-
- Olin, Robert F.
- Committee members dc:contributor.committeemember
-
- Ball, Joseph A.
- McCoy, Robert A.
- Aull, Charles E.
- Johnson, Lee W.
Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-06192006-125737
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/38643