On the $L^{p}$-spaces of projective limits of probability measures

TL;DR

This paper investigates the structure of $L^{p}$-spaces associated with projective limit measures, utilizing category theory, with applications to Gaussian measures on vector spaces and constructive Quantum Field Theory.

Contribution

It introduces a category theoretical framework to analyze $L^{p}$-spaces of projective limits, specifically applied to Gaussian measures and QFT contexts.

Findings

Characterization of $L^{p}$-spaces for projective limit measures

Application to Gaussian measures on nuclear spaces

Relevance to Osterwalder-Schrader axioms in QFT

Abstract

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.