Sigma-compactness of metric boolean algebras and uniform convergence of frequencies to probabilities
Е. Г. Пыткеев, Michael Khachay · Proceedings of the Steklov Institute of Mathematics · 2011
The topological properties of a pseudometric space defined by a measure are investigated. Criteria of compactness and σ -compactness of this space are proved. A new sufficient condition for the uniform convergence (over an event class) of frequencies to probabilities is proved as a corollary.