THE TRANSFINITE MODULI OF CONDENSERS IN SPACE

Abstract

The authors prove the equality of the transfinite α -modulus and the discrete α -modulus of a condenser in p-space, 0<α ≤ p, p ≥ 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 ≥ 3, the transfinite p-modulus is compared with the conformal modulus.