A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time

Given a sequence [Formula: see text] of measurable functions on a σ-finite measure space such that the integral of each [Formula: see text] as well as that of [Formula: see text] exists in [Formula: see text] , we provide a sufficient condition for the following inequality to hold: [Formula: see tex...

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Autor principal: Kamihigashi, Takashi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5243928/
https://www.ncbi.nlm.nih.gov/pubmed/28163549
http://dx.doi.org/10.1186/s13660-016-1288-5
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author Kamihigashi, Takashi
author_facet Kamihigashi, Takashi
author_sort Kamihigashi, Takashi
collection PubMed
description Given a sequence [Formula: see text] of measurable functions on a σ-finite measure space such that the integral of each [Formula: see text] as well as that of [Formula: see text] exists in [Formula: see text] , we provide a sufficient condition for the following inequality to hold: [Formula: see text] Our condition is considerably weaker than sufficient conditions known in the literature such as uniform integrability (in the case of a finite measure) and equi-integrability. As an application, we obtain a new result on the existence of an optimal path for deterministic infinite-horizon optimization problems in discrete time.
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spelling pubmed-52439282017-02-01 A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time Kamihigashi, Takashi J Inequal Appl Research Given a sequence [Formula: see text] of measurable functions on a σ-finite measure space such that the integral of each [Formula: see text] as well as that of [Formula: see text] exists in [Formula: see text] , we provide a sufficient condition for the following inequality to hold: [Formula: see text] Our condition is considerably weaker than sufficient conditions known in the literature such as uniform integrability (in the case of a finite measure) and equi-integrability. As an application, we obtain a new result on the existence of an optimal path for deterministic infinite-horizon optimization problems in discrete time. Springer International Publishing 2017-01-18 2017 /pmc/articles/PMC5243928/ /pubmed/28163549 http://dx.doi.org/10.1186/s13660-016-1288-5 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Kamihigashi, Takashi
A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time
title A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time
title_full A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time
title_fullStr A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time
title_full_unstemmed A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time
title_short A generalization of Fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time
title_sort generalization of fatou’s lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5243928/
https://www.ncbi.nlm.nih.gov/pubmed/28163549
http://dx.doi.org/10.1186/s13660-016-1288-5
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