On the Interchange of Subdifferentiation and Conditional Expectation for Convex Functionals

Rockafellar, R.T. & Wets, R.J.-B. (1981). On the Interchange of Subdifferentiation and Conditional Expectation for Convex Functionals. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-81-089

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Abstract

We show that the operators E^G (conditional expectation given a tau-field G) and partial (subdifferentiation), when applied to a normal convex integrand f, commute if the effective domain multifunction omega -> {x E R^n | f(omega , x) < +infinity } is G-measurable.

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