Displaying similar documents to “Some problems in the algebra of Borel measures”

Coordinatewise decomposition, Borel cohomology, and invariant measures

Benjamin D. Miller (2006)

Fundamenta Mathematicae

Similarity:

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...

Sets with doubleton sections, good sets and ergodic theory

A. Kłopotowski, M. G. Nadkarni, H. Sarbadhikari, S. M. Srivastava (2002)

Fundamenta Mathematicae

Similarity:

A Borel subset of the unit square whose vertical and horizontal sections are two-point sets admits a natural group action. We exploit this to discuss some questions about Borel subsets of the unit square on which every function is a sum of functions of the coordinates. Connection with probability measures with prescribed marginals and some function algebra questions is discussed.