Extension of The Best Approximation Operator in Orlicz Spaces

Abstract EN

Let (Ω,?,μ) be a probability space and ℒ⊂? a sub-σ-lattice of the σ-algebra ?.

We study an extension of the best ϕ-approximation operator from an Orlicz space Lϕ to the space Lϕ′, where ϕ′ denotes the derivative of the convex, but not necessarily a strictly convex function ϕ.

We obtain convergence results when a sequence of σ-algebras ℬn converges to ℬ∞ in a suitable way.