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On the difference between Malliavin derivative and Gross-Sobolev derivative

Let $W=C_0([0,1],\mathbb R^d)$ be the classical Wiener space equipped with $\mu$ the Wiener measure. If $F:W\to\mathbb R$ is a cylindrical function of the form \begin{align*} F(w)=f(W_{t_1}(w),\cdots,...
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References about distances between singular probability measures

I would be interested in references on the topic of distances between probability measures that are singular with one another and not reduced to trivial ones. For example from here we know that total ...
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