Geodesic
On Maslov regularizability of discontinuous mappings
Izvestiya. Mathematics , Tome 42 (1994) no. 1, pp. 27-49

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The concept of a Maslov regularizing algorithm (MRA) is introduced in this paper for an arbitrary mapping $f\colon D(f)\subset X\to Y$ acting in metric spaces $X$ and $Y$, with domain $D(f)$. A necessary condition and a sufficient condition are given for there to be a continuous MRA for $f$. In the case of a separable Banach space $Y$ the set of such mappings is confined to $B$-measurable mappings of first class defined on $F_{\sigma\delta}$-sets. 
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     author = {E. N. Domanskii},
     title = {On {Maslov} regularizability of discontinuous mappings},
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     language = {en},
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}
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E. N. Domanskii. On Maslov regularizability of discontinuous mappings. Izvestiya. Mathematics , Tome 42 (1994) no. 1, pp. 27-49. http://geodesic.mathdoc.fr/item/IM2_1994_42_1_a1/