Modules of Families of Vector Measures on a Riemann Surface

Abstract

The paper considers a Riemann surface (in a broad sense of the term in the Hurwitz–Courant terminology) and an open set with a compact closure on this surface. It is proved that, following Aikawa–Ohtsuka, with a condenser on a given open set one can associate a family of vector measures, whose modules are computed directly with the aid of the weighted capacity (with Muchenhoupt weight) of the condenser.