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For infinite-dimensional Gaussian measures, we often see the definition of Gaussian random variables like this: Let $H(\Omega;\mathbb{R})$ be a separable Hilbert space. A random variable $u \in H$ is ...

The space of temperate distributions $S'(\mathbb{R}^d)$ is often equipped with the weak-$\ast$ or with the strong topology. When defining the notion of a probability measure on $S'(\mathbb{R}^d)$, ...

I am in the process of writing some self-contained notes on probability theory in spaces of distributions, for the purposes of statistical mechanics and quantum field theory. Perhaps the simplest ...

Let $X$ be a Polish space. Let $J\in\mathbb{N}$. Let $\lbrace a^n_1\rbrace_n,\dots,\lbrace a^n_J\rbrace_n$ be $J$ sequences of reals. Let $\lbrace \mu^n_1\rbrace_n,\dots,\lbrace \mu^n_J\rbrace_n$ be ...