Extension of the best approximation operator in Orlicz spaces

Let (Omega, A, mu) be a probability space and L subset of A a sub-sigma-lattice of the sigma-algebra A. We study an extension of the best phi-approximation operator from an Orlicz space L(phi) to the space L(phi)', where phi' denotes the derivative of the convex, but not necessarily a strictly convex function phi. We obtain convergence results when a sequence of sigma-algebras B(n) converges to B(infinity) in a suitable way. Copyright (c) 2008 Ivana Carrizo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.