Stability in the Cauchy and Morera theorems for holomorphic functions and their spatial analogs

Criteria are given for a mapping to have bounded distortion in terms of an integral estimate of the multiplicity function without any a priori assumption on the differential properties of the mapping. The result is most lucid and final in a sense for complex functions $f\colon\Delta\subset\mathbb{C}\to\mathbb{C}$ of one complex variable. Generalizations to multidimensional Beltrami systems are suggested.