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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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/

[1] Vapnik V. N., Chervonenkis A. Ya., Teoriya raspoznavaniya obrazov, Nauka, M., 1974, 528 pp. | MR | Zbl

[2] Vapnik V. N., Statistical learning theory, Wiley, New York, 1998, 740 pp. | MR | Zbl

[3] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, Izd-vo inostr. lit., M., 1952, 896 pp.

[4] Birkgof G., Teoriya reshetok, Nauka, M., 1984, 568 pp. | MR

[5] Kadets V. M., Kurs funktsionalnogo analiza, Izd-vo Khark. natsional. un-ta, Kharkov, 2004, 504 pp.

[6] Borovkov A. A., Matematicheskaya statistika, Nauka, Novosibirsk; Izd-vo Instituta matematiki SO RAN, Novosibirsk, 1997, 772 pp. | MR | Zbl