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We prove the equivalence of two different types of capacities in abstractWiener spaces. This yields a criterion for the $L^p$-uniqueness of theOrnstein-Uhlenbeck operator and its integer powers defined on suitable algebrasof functions vanishing in a neighborhood of a given closed set $\Sigma$ of zeroGaussian measure. To prove the equivalence we show the$W^{r,p}(B,\mu)$-boundedness of certain smooth nonlinear truncation operatorsacting on potentials of nonnegative functions. We also give connections toGaussian Hausdorff measures. Roughly speaking, if $L^p$-uniqueness holds thenthe 'removed' set $\Sigma$ must have sufficiently large codimension, in thecase of the Ornstein-Uhlenbeck operator for instance at least $2p$.

Capacities, removable sets and $L^p$-uniqueness on Wiener spaces