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The Luzin approximation of functions from classes W p α on metric spaces with measure

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Abstract

In this paper we prove an analog of the Luzin theorem on correction for spaces of the Sobolev type on an arbitrary metric space with a measure, satisfying the doubling condition. The correcting function belongs to the Hölder class and approximates a given function in the metrics of the initial space. Dimensions of exceptional sets are evaluated in terms of Hausdorff capacities and volumes.

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Authors and Affiliations

  1. Belarussian State University, pr. F. Skoriny 4, Minsk, 220036, Republic of Belarus

    V. G. Krotov & M. A. Prokhorovich

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  1. V. G. Krotov
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  2. M. A. Prokhorovich
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Correspondence to V. G. Krotov.

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Dedicated to the memory of Petr Lavrent’evich Ul’yanov

Original Russian Text © V.G. Krotov and M.A. Prokhorovich, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 5, pp. 55–66.

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Krotov, V.G., Prokhorovich, M.A. The Luzin approximation of functions from classes W p α on metric spaces with measure. Russ Math. 52, 47–57 (2008). https://doi.org/10.3103/S1066369X0805006X

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