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- W2069059622 abstract "If (xn) is a monotone sequence of reals that is uniformly distributed mod 1, then it is shown that necessarily limn→∞ |xn|/log n = ∞. In fact, this result is obtained as a corollary of a general result on uniform distribution of monotone sequences with respect to probability measures on R/Z and weighted means. We show also that this general result is in a sense best possible. Furthermore, we obtain a characterization of those weighted means that admit uniformly distributed sequences." @default.
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- W2069059622 date "1984-01-01" @default.
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- W2069059622 title "Distribution mod 1 of monotone sequences" @default.
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- W2069059622 doi "https://doi.org/10.1016/1385-7258(84)90031-3" @default.
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