On the \(L^{p}\)-Spaces of Projective Limits of Probability Measures

The present article describes the precise structure of the \(L^{p}\) $L^p$ -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.