  In the first part of the paper we prove various results on regularity of
Feynman-Kac functionals of Hunt processes associated with time dependent
semi-Dirichlet forms. In the second part we study the Cauchy problem for
semilinear parabolic equations with measure data involving operators associated
with time-dependent forms. Model examples are non-symmetric divergence form
operators and fractional laplacians with possibly variable exponents. We first
introduce a definition of a solution resembling Stampacchia's definition in the
sense of duality and then, using the results of the first part, we prove the
existence, uniqueness and regularity of solutions of the problem under mild
assumptions on the data.
