Isotonic Approximation in L1 Original Research Article

Let (Ω,A,P) be a measurable space and L⊂A a sub-σ-lattice of the σ-algebra A. For X∈L1(Ω,A,P) we denote by PLX the set of conditional 1-mean (or best approximants) of X given L1(L) (the set of all L-measurable and integrable functions). In this paper, we obtain characterizations of the elements in PLX, similar to those obtained by Landers and Rogge for conditional s-means with 1