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Projection onto manifold of Gaussian measures by "trunction" of moments

Let $\mathcal{P}_2(\mathbb{R}^n)$ be the set of Borel probability measures on $\mathbb{R}^n$ with finite mean and variance; in the sense that $$ \int_{x \in \mathbb{R}^n} \|x\|^p d\mathbb{P}(x) < \...
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