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Let $X$ be a standard Borel space, so that the space of Borel probability measures on $X$ is also a standard Borel space. We denote it by $\mathcal P(X)$. In this paper for any family of probability ...

Let $X$ be a random variable with the distribution $F$ (cdf). What are the extreme points of the sets of the form: \begin{align} P_1&=\left\{ F: \int |x|^k dF\le c \right\},\\ P_2&=\left\{ F:...