Let (U_{alpha}) be the (alpha)-potential operator of a (mathrm{BM}^{d}). Give a probabilistic interpretation of (U_{alpha} mathbb{1}_{C}) and

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Let \(U_{\alpha}\) be the \(\alpha\)-potential operator of a \(\mathrm{BM}^{d}\). Give a probabilistic interpretation of \(U_{\alpha} \mathbb{1}_{C}\) and \(\lim _{\alpha ightarrow 0} U_{\alpha} \mathbb{1}_{C}\) if \(C \subset \mathbb{R}^{d}\) is a Borel set.

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