The transfinite moduli of condensers in space (Q1092282)

The authors prove the equality of the transfinite \(\alpha\)-modulus and the discrete \(\alpha\)-modulus of a condenser in p-space, \(0<\alpha \leq p\), \(p\geq 3\). Two extremal properties for the transfinite modulus of the Teichmüller ring are deduced from an expansion-contraction property of condensers. For the important examples of the spherical annulus and a ring of Grötzsch type in p-space, \(p\geq 3\), the transfinite p-modulus is compared with the conformal modulus.