Fine properties of functions from Hajłasz–Sobolev classes M α p , p > 0, II. Lusin’s approximation
Tóm tắt
The present paper is devoted to the Lusin’s approximation of functions from Hajłasz–Sobolev classes M
(X) for p > 0. It is proved that for any f ∈ M
(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
(X) and it is a locally Hölder function), and it approximates the original function in the metric of the space M
(X).
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