Abstract
We determine sufficient conditions for the closedness of sum spaces of L 1-functions. As a consequence of Csiszar's projection theorem this implies generalizations of results of Fortet, Beurling and Hobby and Pyke on the existence and uniqueness of solutions of some nonlinear integral equations, which were introduced by Schrödinger, to describe the most probably behaviour of Brownian motions conditional on the observed initial and final state in a finite interval (0, t 1). The results is also of interest for a large deviation formula for infinite dimensional Brownian motions related to Schrödinger bridges and for the construction of optimal estimators in marginal models.
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