On measurability properties connected with the superposition operator.
type: Item
instance of: scholarly article
title: On measurability properties connected with the superposition operator.
zbMATH Open document ID: 1070.28001
author: Alexander Kharazishvili
published in: Real Analysis Exchange
publication date: 2004-08-06T00:00:00Z
review text: Let \(F\) be a class of real-valued functions defined on some set \(E\), measurable with respect to a \(\sigma\)-algebra \(S\). A function \(\phi: E\times\mathbb{R}\to \mathbb{R}\) is called to be sup-measurable with respect to \(F\) if for each \(f\in F\) the function \(\phi_f\) defined by \(\phi_f(x)= \phi(x,f(x))\) is \(S\)-measurable. The main result of the paper is Theorem 1 describing the maximal family \(F'\supset F\) consisting also of \(S\)-measurable functions such that \(\phi\) is sup-measurable with respect to \(F'\). There are also numerous examples explaining the role of axioms of set theory in questions concerning sup-measurability.
Mathematics Subject Classification ID: 28A20
Mathematics Subject Classification ID: 47H30
zbMATH DE Number: 2084031
zbMATH Keywords: sup-measurable functions
zbMATH Keywords: measurability
reviewed by: Władysław Wilczyński
MaRDI profile type: Publication
full work available at URL: realanalexch.28.1.0205
OpenAlex ID: W1599452133
DOI: 10.14321/REALANALEXCH.28.1.0205
description: scientific article; zbMATH DE number 2084031