Approximation of integrable, approximately continuous functions on \((0,1)^ n\) by nondecreasing functions
type: Item
instance of: scholarly article
title: Approximation of integrable, approximately continuous functions on \((0,1)^ n\) by nondecreasing functions
zbMATH Open document ID: 0732.41018
author: Shusheng Fu
author: Richard B. Darst
published in: Real Analysis Exchange
publication date: 1989-01-01T00:00:00Z
review text: The main emphasis of this paper is on the convergence of sequences of best monotone approximations of integrable, absolutely continuous functions on \((0,1)^ n\) in the \(L_ 1\) norm. The first result concerns the best nondecreasing \(L_ 1\) approximation \(f_ 1\) to an approximately continuous function f. It is shown that if the sequence \(f^ m\) converges to \(f_ 1\) in the \(L_ 1\) norm, then \(f^ m_ 1\) also converges to \(f_ 1\) in the \(L_ 1\) norm. The second result concerns the best nondecreasing \(L_ p\) approximation \(f_ p\) to an approximately continuous function f. It is shown that \(f_ p\) converges to \(f_ 1\) a.e. and in the \(L_ 1\) norm as p converges to 1.
Mathematics Subject Classification ID: 41A30
zbMATH DE Number: 4210758
zbMATH Keywords: best monotone approximations
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description: scientific article; zbMATH DE number 4210758