An extension theorem of Baire 1 functions of several variables
type: Item
instance of: scholarly article
title: An extension theorem of Baire 1 functions of several variables
zbMATH Open document ID: 0714.26005
author: Rosalba Carrese
published in: Ricerche di Matematica
publication date: 1988-01-01T00:00:00Z
review text: The main result of the paper is the following theorem: If u is Baire one on \({\mathbb{R}}^ k\) and \(H\subset {\mathbb{R}}^ k\) is a set of k-dimensional Lebesgue measure zero, then there exists a function f such that each \(x\in {\mathbb{R}}^ k\) is a Lebesgue point of f and \(u(x)=f(x)\) for \(x\in H\). This is a k-dimensional version of a theorem of \textit{G. Petruska} and \textit{M. Laczkovich} [Acta Math. Sci. Hung. 25, 189-212 (1974; Zbl 0279.26003)].
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 26B35
zbMATH DE Number: 4175296
zbMATH Keywords: Baire 1 functions of several variables
zbMATH Keywords: extension
reviewed by: Władysław Wilczyński
MaRDI profile type: Publication
Recommended article: Extension of continuous functions to Baire-one functions
Recommended article: An extension of the Darboux property and some typical properties of Baire-1 functions
Recommended article: On the extension of functions of the first Baire class
Recommended article: A generalization of a Baire theorem concerning barely continuous functions
Recommended article: Linear extensions of some Baire-one functions
Recommended article: A characterization of Baire one functions of two variables
Recommended article: On some properties of Baire-1 functions
Recommended article: Extending Baire-one functions on compact spaces
Recommended article: Extensions of discrete and equal Baire functions
Recommended article: Q3834792
description: scientific article; zbMATH DE number 4175296