The Feynman measure as a limit of complex measures

The fundamental solution of the Schrödinger equation for a free particle is a distribution. Such distribution is approximated by a sequence of smooth functions. For each one of these functions it is defined a complex measure on the space of paths. For certain test functions, there exists the limit of integrals of a test function with respect to the complex measures. We define the Feynman measure of one such function by this limit.