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Vector measures of various smoothness classes and their limits

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Abstract

A relationship between different types of continuity with respect to direction and other types of smoothness is found for vector measures. The following problem is also studied: What vector measures can be represented as the limits of quasiinvariant, infinitely differentiable, analytic, and continuous measures in the topologies of convergence in variation, convergence in semivariation, and convergence on every measurable set.

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Authors and Affiliations

  1. Kirovograd Pedagogical Institute, Kirovograd

    V. A. Romanov

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  1. V. A. Romanov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 512–516, April, 1995.

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Romanov, V.A. Vector measures of various smoothness classes and their limits. Ukr Math J 47, 594–598 (1995). https://doi.org/10.1007/BF01056045

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  • DOI: https://doi.org/10.1007/BF01056045

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