Borel-Cantelli Lemma

Abstract

This article is about the Borel-Cantelli Lemma in probability theory. Necessary definitions and theorems are given in [10] and [7].Ludwig Maximilians University of Munich, GermanyGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Fuguo Ge and Xiquan Liang. On the partial product of series and related basic inequalities. Formalized Mathematics, 13(3):413-416, 2005.Hans-Otto Georgii. Stochastik, Einführung in die Wahrscheinlichkeitstheorie und Statistik. deGruyter, Berlin, 2 edition, 2004.Adam Grabowski. On the Kuratowski limit operators. Formalized Mathematics, 11(4):399-409, 2003.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Achim Klenke. Wahrscheinlichkeitstheorie. Springer-Verlag, Berlin, Heidelberg, 2006.Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.Jarosław Kotowicz. The limit of a real function at infinity. Formalized Mathematics, 2(1):17-28, 1991.Andrzej Nędzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.Andrzej Nędzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.Konrad Raczkowski and Andrzej Nędzusiak. Series. Formalized Mathematics, 2(4):449-452, 1991.Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Limit of sequence of subsets. Formalized Mathematics, 13(2):347-352, 2005.Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Set sequences and monotone class. Formalized Mathematics, 13(4):435-441, 2005