Convergence theorems for partial sums of arbitrary stochastic sequences.
Wang, Xiaosheng, Guo, Haiying (2010)
Journal of Inequalities and Applications [electronic only]
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Convergence theorems for partial sums of arbitrary stochastic sequences.
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The notion of -convergence of a sequence of functions is stronger than pointwise convergence and weaker than uniform convergence. It is inspired by the investigation of ill-posed problems done by A.N. Tichonov. We answer a question posed by M. Katětov around 1970 by showing that the only analytic metric spaces for which pointwise convergence of a sequence of continuous real valued functions to a (continuous) limit function on implies -convergence are -compact spaces. We show that...