Abstract
Let (pn) be a monotonically increasing sequence of numbers. Two examples are given of weights (pn) with the Borel property (i.e. almost all sequences are (pn)-uniformly distributed). In the first one, there exists a (pn) - u.d. sequence (xm) such that \((x_{m_n } )\) is not (pn) - u.d. for almost all subsequences (mn). In the second one, there exists a non-(pn)-u.d. sequence (xn) such that \((x_{m_n } )\) is (pn)-u.d. for almost all subsequences (mn).
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Literatur
KEOGH F.R., PETERSEN G.M.: Riesz summability of subsequences, Quarterly J.Math. Oxford (2), 12 (1961), 33–44.
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© 1985 Springer-Verlag
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Losert, V. (1985). Gleichverteilte Folgen Und Folgen, Für Die Fast Alle Teilfolgen Gleichverteilt Sind. In: Hlawka, E. (eds) Zahlentheoretische Analysis. Lecture Notes in Mathematics, vol 1114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101648
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DOI: https://doi.org/10.1007/BFb0101648
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