Geodesic
The Luzin approximation of functions from the classes $W^p_\alpha$ on metric spaces with measure
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 55-66

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In this paper we prove an analog of the Luzin theorem on correction for the Sobolev-type spaces on an arbitrary metric space, whose measure satisfies 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 volumes and capacities.
Keywords: a metric space with a measure, Luzin approximation.
Mots-clés : Sobolev spaces 
@article{IVM_2008_5_a6,
     author = {V. G. Krotov and M. A. Prokhorovich},
     title = {The {Luzin} approximation of functions from the classes $W^p_\alpha$ on metric spaces with measure},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {55--66},
     publisher = {mathdoc},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_5_a6/}
}
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V. G. Krotov; M. A. Prokhorovich. The Luzin approximation of functions from the classes $W^p_\alpha$ on metric spaces with measure. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2008), pp. 55-66. http://geodesic.mathdoc.fr/item/IVM_2008_5_a6/