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Rearrangements of series in Lp

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Abstract

In this note we show that the condition

$$\sqrt {\sum\nolimits_{n = 1}^\infty {f_n^2 (x)} } \in L_p$$

is sufficient for the set of sums of the rearranged series ∑σ fn to be a closed linear set in Lp.

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Literature cited

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    E. M. Nikishin

Authors
  1. E. M. Nikishin
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Additional information

Translated from Matematicheskie Zametki, Vol. 14, No. 1, pp. 31–38, July, 1973.

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Nikishin, E.M. Rearrangements of series in Lp . Mathematical Notes of the Academy of Sciences of the USSR 14, 570–574 (1973). https://doi.org/10.1007/BF01095771

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  • DOI: https://doi.org/10.1007/BF01095771

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