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Let fXn; nb 1g be an arbitrary sequence of dependent absolutely con- tinuous random viariables, fBn; nb 1g be Borel sets on the real line, and IBn ðxÞ be the indicator function of Bn. In this paper, the limit properties of fIBn ðXnÞ; nb 1g are studied, and a kind of strong limit theorem represented by inequalities with random bounds is obtained.

A strong limit theorem expressed by inequalities for the sequences of absolutely continuous random variables