Answer by Stéphane Laurent for Existence of a conditional expectation...
If $X$ is a random variable on an arbitrary probability space $(\Omega, \mathcal{A}, \mathbb{P})$ and taking its values in a standard Borel space $\mathbb{X}$, and $\mathcal{B} \subset \mathcal{A}$ is...
View ArticleAnswer by geetha290krm for Existence of a conditional expectation...
What you want is $d(X,z)1_A=0$ a.s (because of non-negativity) and, in particular, this must holds for $A=\Omega$. So this is possible only if $X$ is a.s. equal to some $Z$ which is $\mathcal G-$...
View ArticleExistence of a conditional expectation construction for metric spaces
Following the construction of the conditional expectation for real valued random variables, I wondered if it can be 'generalized' to metric spaces as follows. Let $(\mathbb{X}, d)$ be a metric space,...
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