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Let $\mu$ be a centred Radon Gaussian measure on a locally convex space $X$ and $q : X \to \mathbb{R}$ a seminorm that is $\mathcal{B}(X)_\mu$-measurable, where $\mathcal{B}(X)_\mu$ is the Lebesgue co …

I have found an answer exploiting the equivalence of Lusin and Borel measurability as stated in Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures on page 6, theorem 5: Let $H : …

I have a Fréchet space $V$ whose topology is (if it helps) induced by a family $\mathcal{P}$ of norms - not just seminorms - and on this space I have a Borel probability measure $\nu$. Now, I would li …

A more abstract version of this theorem can be found in Le théorème de continuité de P. Lévy sur les espaces nucléaires where it is proven for Borel measures on strict inductive limits of nuclear Fréc …

Everything below is to be viewed in the Euclidean setting with $d$ dimensions and all measures are understood to be Borel measures. The usual problem of Quantum Field Theory is to make sense of Feynma …

I recently came across the very nice review "Differentiable Measures and the Malliavin Calculus" by Bogachev (1997) which begins by discussing measures $\mu$ on locally convex spaces $X$ with the prop …

If we consider the usual formal construction of a path integral over fields with gauge symmetries e.g as in Weinbergs "The Quantum Theory of Fields - Volume 2" the notion of gauge invariance is clear …