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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 046.35203

**Autor: ** Chung, Kai Lai; Erdös, Pál

**Title: ** On the application of the Borel-Cantelli lemma. (In English)

**Source: ** Trans. Am. Math. Soc. 72, 179-186 (1952).

**Review: ** Let a sequence of events E_{k} be given and define **limsup** E_{k} by \cap_{n = 1}^{oo} \cup_{k = n}^{oo} E_{k}. The authors state conditions for the probability of lim **limsup** E_{k} to be unity. Their assumptions do not include independence of the events (as the Borel-Cantelli lemma does) and they are weaker than Borel's condition **sum** P (E_{k} | \bar E_{1},...\bar E_{k-1}) = oo. The result is applied to independent random variables which take the values ± 1 with probabilities ^{1}/_{2} .

**Reviewer: ** St.Vajda

**Classif.: ** * 60D05 Geometric probability

**Index Words: ** probability theory

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