Approximation of vector valued functions
type: Item
instance of: scholarly article
title: Approximation of vector valued functions
zbMATH Open document ID: 0909.46018
DOI: 10.1023/A:1009735326768
published in: Positivity
publication date: 1999-04-08T00:00:00Z
review text: It is known that a lower semi-continuous function from a metric space to \([0,\infty)\) can be approximated by an increasing sequence of Lipschitz continuous functions. This is generalized to a class of vector lattice valued functions. For a complete Banach lattice \(E\), an extension \(E^*\) is considered by adjoining an ``\(\infty\)''. An appropriate type of continuity, called inf-continuity, is considered in proving approximation results. The Lipschitz approximation leads to the consideration of a variational inferior limit and a convergence concept called \(V\)-convergence. Various results describing convergence are provided and these results are applied to obtain stochastic theorems.
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 1121766
zbMATH Keywords: Lipschitz approximation
zbMATH Keywords: lower semi-continuous function
zbMATH Keywords: Lipschitz continuous functions
zbMATH Keywords: complete Banach lattice
zbMATH Keywords: inf-continuity
zbMATH Keywords: variational inferior limit
zbMATH Keywords: \(V\)-convergence
zbMATH Keywords: stochastic theorems
author: Vincent Jalby
reviewed by: William A. Feldman
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1121766