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Sequences of closed sets of bounded variation converging in the deviation metric

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Abstract

From an arbitrary convergent sequence of sets of bounded variation we can select a subsequence such that there is convergence in almost every hyperplane.

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Literature cited

  1. A. G. Vitushkin, Multidimensional Variations of Sets [in Russian], Moscow (1954).

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Authors and Affiliations

  1. Dagestan Polytechnic Institute, USSR

    V. S. Meilanov

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  1. V. S. Meilanov
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Translated from Matematicheskie Zametki, Vol. 15, No. 4, pp. 521–526, April, 1974.

The author thanks A. G. Vitushkin and M. S. Mel'nikov for their constant interest in his work.

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Meilanov, V.S. Sequences of closed sets of bounded variation converging in the deviation metric. Mathematical Notes of the Academy of Sciences of the USSR 15, 305–308 (1974). https://doi.org/10.1007/BF01095118

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  • DOI: https://doi.org/10.1007/BF01095118

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