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In this paper we analyze relations among several types of convergences of bounded sequences, in particulars among statistical convergence, -convergence, -convergence, almost convergence, strong -Cesàro convergence and uniformly strong -Cesàro convergence.
We characterize statistical independence of sequences by the -discrepancy and the Wiener -discrepancy. Furthermore, we find asymptotic information on the distribution of the -discrepancy of sequences.
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