  We show that every operator in $L^{2}$ has an associated measure on a space
of functions and prove that it can be used to find solutions to abstract Cauchy
problems, including partial differential equations. We find explicit formulas
to compute the integral of functions with respect to this measure and develop
approximate formulas in terms of a perturbative expansion. We show that this
method can be used to represent solutions of classical equations, such as the
diffusion and Fokker-Plank equations, as Wiener and
Martin-Siggia-Rose-Jansen-de Dominics integrals, and propose an extension to
paths in infinite dimensional spaces.
