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Selection principles for maps of several variables

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Abstract

We show that a pointwise precompact sequence of maps from the n-dimensional rectangle into a metric semigroup, whose total variations in the sense of Vitali, Hardy and Krause are uniformly bounded, contains a pointwise convergent subsequence. We present a variant of this result for maps with values in a reflexive separable Banach space with respect to the weak pointwise convergence of maps.

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Authors and Affiliations

  1. State University Higher School of Economics in Nizhni Novgorod, Nizhni Novgorod, Russia

    V. V. Chistyakov & Yu. V. Tretyachenko

Authors
  1. V. V. Chistyakov
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  2. Yu. V. Tretyachenko
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Additional information

Published in Russian in Doklady Akademii Nauk, 2010, Vol. 431, No. 5, pp. 598–601.

The article was translated by the authors.

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Chistyakov, V.V., Tretyachenko, Y.V. Selection principles for maps of several variables. Dokl. Math. 81, 282–285 (2010). https://doi.org/10.1134/S106456241002033X

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