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user 313861
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$L^p$-barycenters via continuous selectors
There exists a minimizer for all $p\in [1,\infty[$. To see that, let $R > 0$ be big enough so that
$$
\int_{B_R(0)}\|u\|^pd\mathbb{P}(u) > \frac{1}{2}\int_{\mathbb{R}^n}\|u\|^pd\mathbb{P}(u).
$$
Then …
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