Upper and lower approximations of Perron integrable functions
type: Item
instance of: scholarly article
title: Upper and lower approximations of Perron integrable functions
zbMATH Open document ID: 0941.26006
published in: Real Analysis Exchange
publication date: 2000-05-22T00:00:00Z
review text: A characterization of Perron integrability of a function \(f:[a,b] \to \overline {\mathbb R}\) is given using upper and lower approximations of \(f\) which are lower and upper semi-Baire \(1\). For example: \(f\) is Perron integrable if and only if for every \(\varepsilon >0\) there exist two integrable functions \(g_\varepsilon \) and \(h_\varepsilon \) which are upper and lower semi-Baire \(1 \), respectively, \(g_\varepsilon < \infty \), \(h_\varepsilon >-\infty \), \(g_\varepsilon \leq f\leq h_\varepsilon \) and \(\int _a^b(h_\varepsilon - g_\varepsilon) <\varepsilon \).
reviewed by: Štefan Schwabik
Mathematics Subject Classification ID: 26A39
Mathematics Subject Classification ID: 26A21
zbMATH DE Number: 1450287
zbMATH Keywords: Perron integral
zbMATH Keywords: approximation
zbMATH Keywords: semi-Baire 1 functions
author: C. Faure
author: Francois Guenard
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1450287