  An approach to infinite dimensional integration which unifies the case of
oscillatory integrals and the case of probabilistic type integrals is
presented. It provides a truly infinite dimensional construction of integrals
as linear functionals, as much as possible independent of the underlying
topological and measure theoretical structure. Various applications are given,
including, next to Schr\"odinger and diffusion equations, also higher order
hyperbolic and parabolic equations.
