Convex Stochastic Duality and the "Biting Lemma"

A standard approach to duality in stochastic optimization problems with constraints in

relies upon the Yosida - Hewitt theorem. We develop an alternative technique which employs only "elementary" means. The technique is based on an

\varepsilon ε

-regularization of the original problem and on passing to the limit as

\varepsilon \to 0 ε → 0

with the help of a simple measure-theoretic fact – the biting lemma.