Daniell-Loomis integrals
type: Item
instance of: scholarly article
title: Daniell-Loomis integrals
zbMATH Open document ID: 0911.28011
published in: Rocky Mountain Journal of Mathematics
publication date: 1999-04-26T00:00:00Z
full work available at URL: CONT27-4.html
review text: An integral extension of Lebesgue power, for arbitrary nonnegative linear functionals on functions vector lattices, was discussed by \textit{P. Bobillo Guerrero} and \textit{M. Díaz Carrillo} [Arch. Math. 49, 245-256 (1987; Zbl 0612.28010); ibid. 52, No. 3, 258-264 (1989; Zbl 0674.28005)]. Here, this extension process is generalized by ``localization'', using an appropriate local convergence in measure that has also been used to prove convergence theorems. Various descriptions of the set of integrable functions are also given, and in particular, a Darboux type characterization is stated. Riemann-\(\mu\), abstract Riemann-Loomis and Bourbaki integrals are subsumed.
Mathematics Subject Classification ID: 28C05
Mathematics Subject Classification ID: 26A42
zbMATH DE Number: 1206687
zbMATH Keywords: Loomis integral
zbMATH Keywords: convergence theorems
zbMATH Keywords: abstract Riemann-Loomis integral
zbMATH Keywords: Bourbaki integral
author: Manuel Díaz Carrillo
author: Hans Günzler
reviewed by: P. Jiménez Guerra
MaRDI profile type: Publication
OpenAlex ID: W2041364043
cites work: Integralerweiterungen mittels Normen
cites work: Summable and integrable functions with respect to any Loomis-system
cites work: On the summability of certain \(\mu\)-integrable functions
cites work: The Daniell-Bourbaki Integral for Finitely Additive Measures
cites work: Linear functionals which are integrals
cites work: Q3989551
cites work: Q4135809
cites work: Linear Functionals and Content
cites work: Q4135806
cites work: Lokale Integralnomen und verallgemeinerte uneigentliche Riemann-Stieltjes-Integrale.
DOI: 10.1216/RMJM/1181071861
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description: scientific article; zbMATH DE number 1206687