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Hausdorff measures on the Wiener space

Potential Analysis, 1992
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Feyel, D., de La Pradelle, A.
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Wasserstein space over the Wiener space

Probability Theory and Related Fields, 2009
Define on an abstract Wiener space \((X,H,\mu)\) the lower semicontinuous distance \(d_H(x,y)=|x-y|_H\) if \(x-y\in H\) and \(d_H(x,y)=\infty\) otherwise. On the space of probability measures \({\mathcal P}(X)\) on \(X\) one considers the Wasserstein distance \[ W_s(\nu_1,\nu_2)^2:= \inf\left\{ \int_{X\times X} |x-y|_H^2\pi(dx,dy),\;\pi\in{\mathcal P ...
Fang, Shizan   +2 more
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