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Some continuity issues of the optimal transport map (Brenier map)

$\newcommand{\si}{\sigma}\newcommand{\W}{\mathcal W}\newcommand{\R}{\mathbb R} $Yes, the map \begin{equation*} \mu \mapsto J(\mu):=\int_\R T^\si_\mu(x+y)\exp(-y^2/2\si^2)\,dy \tag{10}\label{10} \...
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