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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

8 votes
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179 views

Distribution domination for sums of independent random variables in Banach spaces

Let $X$ be a Banach space and let $(\xi_n)$ and $(\eta_n)$ be independent mean-zero random variables with values in $X$ satisfying $$ \sum_n \mathbb P(\xi_n \in A) \leq \sum_n \mathbb P(\eta_n \in A), …