The Hake's property for some integrals over multidimensional intervals
type: Item
instance of: scholarly article
title: The Hake's property for some integrals over multidimensional intervals
zbMATH Open document ID: 0832.26010
published in: Real Analysis Exchange
publication date: 1996-02-13T00:00:00Z
review text: The Hake's property for a one-dimensional Perron-Denjoy integral is the equivalence between the integrability of a function over \([a,b]\) and its integrability over \([a,c]\) for all \(c \in ]a,b[\) and the existence of the limit \(\lim_{c \to b -} \int^c_af\). For a real function \(f\) defined on a compact interval \(I\) of \(\mathbb{R}^n\), and for various types of multidimensional nonabsolute integrals, this note proves the equivalence between the integrability of \(f\) over \(I\) and the integrability of \(f\) over all intervals \(J \subset \text{int} I\) together with the existence of the appropriate limit \(\lim_{F \to \text{int} I} \int_Ff\), where \(F \subset \text{int} I\) is a finite union of compact intervals of \(\mathbb{R}^n\).
Mathematics Subject Classification ID: 26B20
Mathematics Subject Classification ID: 26A39
zbMATH DE Number: 801019
zbMATH Keywords: Hake's property
zbMATH Keywords: multidimensional nonabsolute integrals
author: C. Faure
author: Jean Mawhin
reviewed by: Jean Mawhin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 801019