Coordinatewise decomposition, Borel cohomology, and invariant measures

• Autorzy: Benjamin D. Miller
• Języki publikacji: EN

Abstrakty

EN

Given Polish spaces X and Y and a Borel set S ⊆ X × Y with countable sections, we describe the circumstances under which a Borel function f: S → ℝ is of the form f(x,y) = u(x) + v(y), where u: X → ℝ and v: Y → ℝ are Borel. This turns out to be a special case of the problem of determining whether a real-valued Borel cocycle on a countable Borel equivalence relation is a coboundary. We use several Glimm-Effros style dichotomies to give a solution to this problem in terms of certain σ-finite measures on the underlying space. The main new technical ingredient is a characterization of the existence of type III measures of a given cocycle.

Kategorie tematyczne

• 03E15: Descriptive set theory
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 191
• Numer: 1
• Strony: 81-94

Daty

wydano

2006

Twórcy

autor

Benjamin D. Miller

• Department of Mathematics, University of California, 520 Portola Plaza, Los Angeles, CA, 90095-1555, U.S.A.

Identyfikatory

DOI

10.4064/fm191-1-6