On a problem of S. Mazur
type: Item
instance of: scholarly article
zbMATH Open document ID: 0992.28007
publication date: 2002-02-13T00:00:00Z
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 1703989
zbMATH Keywords: universal measurability
zbMATH Keywords: additive functionals
zbMATH Keywords: functional equations
zbMATH Keywords: The Scottish Book
MaRDI profile type: Publication
author: Antal Járai
title: On a problem of S. Mazur
published in: Publicationes Mathematicae Debrecen
review text: In about 1935 S. Mazur asked the following: An additive functional \(f\) in a Banach space \(X\) is given with the property NEWLINE\[NEWLINE\text{for each path \(g\) in \(X,f\circ g\) is Lebesgue measurable}. \tag{P}NEWLINE\]NEWLINE Is it true that \(f\) is continuous? The author proves that, in certain topological spaces, property (P) is equivalent with universal measurability. This makes possible to use ``measurability implies continuity'' type results, that are known for a large class of functional equations, to get ``property (P) implies continuity''.
description: scientific article; zbMATH DE number 1703989