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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
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The central limit theorem in the subgaussian Orlicz norm
A real random variable $X$ is said to be subgaussian if there exists an $a > 0$ such that $\mathbb{E}[e^{\lambda X}] < e^{a^2 \lambda^2}$ for all $\lambda \in \mathbb{R}$. The space of such random var …