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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

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Continuity of the conditional expectation

Consider the conditional expectation of $x$ given $y$, $$ \mathbb{E}(x | y) $$ where $x \in X$ and $y \in Y$ where $X, Y$ are Hilbert spaces (possibly infinite dimensional). Question : I am looking f …