Gaussian random variable in a Banach space
= Gaussian random variable in a Banach space
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= Banach-valued Gaussian random variable
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{synonym}
A random variable $X$ in a real <separable Banach space> $B$ is Gaussian when $\ell(X)$ has a <normal distribution> for every <continuous linear functional> $\ell\in B^*$. It is centered when all these <expected values> vanish. Its <probability law> is a <Gaussian measure>. Degenerate <normal distributions> are allowed.