The present article describes the precise structure of the $L^{p}$-spaces of projective limit measures by introducing a category theoretical perspective. This analysis is applied to measures on vector spaces and in particular to Gaussian measures on nuclear topological vector spaces. A simple application to constructive Quantum Field Theory (QFT) is given through the Osterwalder-Schrader axioms.
The linear topology associated with weak convergence of probability measures
The Topology of Information on the Space of Probability Measures over Polish Spaces
On spectra of probability measures generated by GLS-expansions
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