Let $\pi_{0}$ and $\pi_{1}$ be two probability measures on $\mathbb{R}^{d}$, equipped with the Borel $\sigma$-algebra $\mathcal{B}(\mathbb{R}^{d})$. Any measurable function $T:\mathbb{R}^{d}\rightarrow\mathbb{R}^{d}$ such that $Y=T(X)\sim\pi_{1}$ if $X\sim\pi_{0}$ is called a transport map from $\pi_{0}$ to $\pi_{1}$... (read more)

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