The error in discrete Phi-approximation
Let phi : [0, infinity) --> [0, infinity) be a convex function phi (x) > 0, if x > 0, phi (0) = 0 and let (Omega, A, mu) be a measure space, where Omega = N or a finite subset of N, A = -2(Omega), and mu is any finite measure. We consider the set MO,W(f) of best monotone phi -approximates of the function f in the Orlicz space L-phi = L-phi(Omega, A, mu). We obtain a best phi -approximant as limit of one sequence of best approximates in finite dimension. Also, we give a computational algorithm to estimate the error in phi -approximation of functions in the subspace L-phi(infinity), by nondecreasing functions. (C) 2001 Elsevier Science Ltd. All rights reserved.
orlicz space monotone approximation