On Maslov regularizability of discontinuous mappings

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.