The Miniowitz and Vuorinen theorems for the mappings with non-bounded characteristics

The present paper is devoted to the study of classes of mappings with non–bounded characteristics of quasiconformality. It is proved that the normal families of mappings distorting the families of mappings in ${\mathbb{R}}^n$ by special way, have the logarithmic order of growth in the neighborhood of every point. There are proved some sufficient conditions of normality of such mappings $f:D\to \overline{{\mathbb{R}}^n},$ $n\ge 2,$ omitting the values of some set $E_f$ with some constraints of the type $c(E_f)\ge \delta ,$ $\delta\in {\Bbb R},$where$c(\cdot)$ is the special set function.