Geodesic
Sigma-compactness of metric Boolean algebras and uniform convergence of frequencies to probabilities
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 127-139

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The topological properties of a pseudometric space defined by a measure are investigated. Criteria of compactness and $\sigma$-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.
Keywords: metric Boolean algebra, sigma-compactness, uniform convergence of frequencies to probabilities over an event class. 
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     title = {Sigma-compactness of metric {Boolean} algebras and uniform convergence of frequencies to probabilities},
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E. G. Pytkeev; M. Yu. Khachai. Sigma-compactness of metric Boolean algebras and uniform convergence of frequencies to probabilities. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 127-139. http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a10/