An invariance result for capacities on Wiener space

AbstractWe prove that tight capacities are invariant if one weakens the underlying topology. As a consequence we obtain a comparison theorem about (r, p)-capacities (and the corresponding notion of (r, p)-quasi-continuity used in the Malliavin calculus) on different abstract Wiener spaces (Ej, H, μj) with common Hilbert space H. Furthermore, we prove tightness of (r, p)-capacities of Ornstein-Uhlenbeck semigroups with general linear drift