Сondensers and equivalent open sets on a Riemann surface

Condensers on the compact closure of an open set on a Riemann surface are studied. The equality of the capacity and module of condenser is proved. The definition of NED-sets on the Riemann surface is given and it is proved that NED-sets do not affect the condenser module. Also, a criterion of equivalence of open sets on the Riemann surface is established.