In this paper we establish
various results involving conditional Wiener integrals, E(F|X), for very general
conditioning functions X. Most related results in the literature, including the case
when the conditioning function X is vector-valued, then follow as corollaries of this
more general theory. A simple formula is given for converting these generalized
conditional Wiener integrals into ordinary Wiener integrals and then this formula is
used to evaluate E(F|X) for various classes of functionals F. Finally these results are
used to obtain a generalized conditional form of the Cameron-Martin translation
theorem.
