ALMOST SURE CONVERGENCE OF SEQUENCES WITH RANDOM INDICES
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概要
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"Let ＄Z_{+}^{d}＄ , where ＄d￥geqq 1＄ is an integer, denote the positive integer d-dimensional lattice points. Let ＄￥{Y_{n}, n￥in Z_{+}^{a}￥}＄ be a set of random variables. Let ＄￥{N_{n}, n￥in Z_{+}^{d}￥}＄ be a set of ＄Z_{+}^{d}＄-valued random variables. In this paper we study almost sure convergence of the random field ＄￥{Y_{N_{n}}, n￥in Z_{+}^{d}￥}＄ as ＄ n￥rightarrow￥infty＄ . We introduce an almost sure version of Anscombe condition and study its consequences in strong limit theorem."
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