On I. P. Mityuk's reduced modulus

We introduce the reduced modulus of an arbitrary open set with respect to several points of the set and some boundary arcs. This generalizes the reduced modulus introduced by I. P. Mityuk in 1964. We study the basic properties of this modulus — its behavior under extension, conformal mapping and the composition principles. As an application, the theorems on non-overlapping domains and the covering theorems under conformal mapping have been generalized.