  This paper proposes a general duality framework for the problem of minimizing
a convex integral functional over a space of stochastic processes adapted to a
given filtration. The framework unifies many well-known duality frameworks from
operations research and mathematical finance. The unification allows the
extension of some useful techniques from these two fields to a much wider class
of problems. In particular, combining certain finite-dimensional techniques
from convex analysis with measure theoretic techniques from mathematical
finance, we are able to close the duality gap in some situations where
traditional topological arguments fail.
