On the lightness of the limit of sequence of mappings satisfying some modular inequality

Abstract

A paper is devoted to study of one class of space mappings which are more general than mappings with bounded distortion. It is showed that a locally uniformly limit of a sequence of mappings $f:D\rightarrow {\Bbb R}^n$ of domain $D\subset{\Bbb R}^n,$ $n\geqslant 2,$ satisfying one inequality with respect to $p$-modulus of families of curves, is light. The above statement is a generalization of well-known theorem about openness and discreteness of uniformly limit of a sequence of mappings with bounded distortion.