Sigma-compactness of metric boolean algebras and uniform convergence of frequencies to probabilities / Pytkeev E.G., Khachai M.Y. // Proceedings of the Steklov Institute of Mathematics. - 2011. - V. 272, l. SUPPL. 1. - P. S138-S151.

ISSN:

00815438

Type:

Article

Abstract:

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. © 2011 Pleiades Publishing, Ltd.

Author keywords:

metric Boolean algebra; sigma-compactness; uniform convergence of frequencies to probabilities over an event class

Index keywords:

нет данных

DOI:

10.1134/S0081543811020118

Смотреть в Scopus:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-79954606200&doi=10.1134%2fS0081543811020118&partnerID=40&md5=4d4510fa3a54f57e6751f0e20bc167f3

Соавторы в МНС:

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Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-79954606200&doi=10.1134%2fS0081543811020118&partnerID=40&md5=4d4510fa3a54f57e6751f0e20bc167f3
Affiliations	Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg 620990, Russian Federation
Author Keywords	metric Boolean algebra; sigma-compactness; uniform convergence of frequencies to probabilities over an event class
References	Vapnik, V.N., Chervonenkis, A.Y., (1974) Pattern Recognition Theory, , Moscow: Nauka; Vapnik, V.N., (1998) Statistical Learning Theory, , New York: Wiley; Dunford, N., Schwartz, J., (1958) Linear Operators: General Theory, , New York: Interscience; Birkhoff, G., (1940) Lattice Theory, , New York: Amer. Math. Soc; Kadets, V.M., (2004) A Course of Functional Analysis, , Kharkiv: Izd. Khar'kovsk. Nats. Univ; Borovkov, A.A., (1997) Mathematical Statistics, , Novosibirsk: Nauka
Correspondence Address	Pytkeev, E. G.; Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg 620990, Russian Federation; email: pyt@imm.uran.ru
Language of Original Document	English
Abbreviated Source Title	Proc. Steklov Inst. Math.
Source	Scopus