Abstract
The present paper is devoted to the Lusin’s approximation of functions from Hajłasz–Sobolev classes M p α (X) for p > 0. It is proved that for any f ∈ M p α (X) and any ε > 0 there exist an open set O ε ⊂ X with measure less than ε (as a measure can be taken the corresponding capacity or Hausdorff content) and an approximating function f ε such that f = f ε on X O ε . Moreover, the correcting function f ε is regular (that is, it belongs to the underlying space M p α (X) and it is a locally Hölder function), and it approximates the original function in the metric of the space M p α (X).
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Original Russian Text © S. A. Bondarev, V. G. Krotov, 2017, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2017, No. 1, pp. 26-37.
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Bondarev, S.A., Krotov, V.G. Fine properties of functions from Hajłasz–Sobolev classes M p α , p > 0, II. Lusin’s approximation. J. Contemp. Mathemat. Anal. 52, 30–37 (2017). https://doi.org/10.3103/S1068362317010046
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DOI: https://doi.org/10.3103/S1068362317010046