All Questions

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 $\mathcal P(X)$ denote the space of all probability measure defined on a measurable space $X$. We canonically endow the former with its own measurability structure, generated by evaluation maps. ...

Let $X$ be a countable set. A lottery on $X$ is a function $\lambda: X \to [0,1]$ such that $\sum_x \lambda(x) = 1$. Let $\Delta X$ be the set of lotteries on $X$. A total preorder $\preceq$ on $\...

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:...

Let $\mu$ be a probability measure on a subset $C \subset \mathbb{R}^\infty$ of the space of sequences, and assume, for simplicity, that $C$ is closed and convex. We say that $\mu$ admits shifts if ...