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The paper is devoted to the study of classes of mappings with non-bounded characteristics of quasiconformality. We prove that the normal families of Q-mappings have the logarithmic order of growth in a neighborhood of a point. Moreover, we establish sufficient conditions for Q to ensure the normality of mappings f: D →  Open image in new window , n ≥ 2, which omit the points of a set E  f . The latter obeys c(E  f ) ≥ δ, δ > 0, where c(·) is an appropriate set function.

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