Egoroff's theorems for random sets on non-additive measure spaces

Egoroff's theorems for random sets on non-additive measure spaces

We present four versions of Egoroff's theorems for measurable closed-valued multifunctions on non-additive measure spaces. The conditions provided for each of these four versions are not only sufficient, but also necessary. In our discussions the continuity of non-additive measures is not requi...

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Main Authors: Tao Chen, Hui Zhang, Jun Li
Format: Article
Language:English
Published: AIMS Press 2021-03-01
Series:AIMS Mathematics
Subjects:
random set
non-additive measure
the egoroff theorem
Online Access:http://www.aimspress.com/article/doi/10.3934/math.2021282?viewType=HTML
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spelling doaj-dd405f52405142b788c025339fd640062021-03-05T01:57:13ZengAIMS PressAIMS Mathematics2473-69882021-03-01654803481010.3934/math.2021282Egoroff's theorems for random sets on non-additive measure spacesTao Chen0Hui Zhang1Jun Li21. School of Data Science and Media Intelligence, Communication University of China, Beijing 100024, China1. School of Data Science and Media Intelligence, Communication University of China, Beijing 100024, China1. School of Data Science and Media Intelligence, Communication University of China, Beijing 100024, China 2. School of Sciences, Communication University of China, Beijing 100024, ChinaWe present four versions of Egoroff's theorems for measurable closed-valued multifunctions on non-additive measure spaces. The conditions provided for each of these four versions are not only sufficient, but also necessary. In our discussions the continuity of non-additive measures is not required. The previous related results are improved and generalized.http://www.aimspress.com/article/doi/10.3934/math.2021282?viewType=HTMLrandom setnon-additive measurethe egoroff theorem
collection DOAJ
language English
format Article
sources DOAJ
author Tao Chen
Hui Zhang
Jun Li
spellingShingle Tao Chen
Hui Zhang
Jun Li
Egoroff's theorems for random sets on non-additive measure spaces
AIMS Mathematics
random set
non-additive measure
the egoroff theorem
author_facet Tao Chen
Hui Zhang
Jun Li
author_sort Tao Chen
title Egoroff's theorems for random sets on non-additive measure spaces
title_short Egoroff's theorems for random sets on non-additive measure spaces
title_full Egoroff's theorems for random sets on non-additive measure spaces
title_fullStr Egoroff's theorems for random sets on non-additive measure spaces
title_full_unstemmed Egoroff's theorems for random sets on non-additive measure spaces
title_sort egoroff's theorems for random sets on non-additive measure spaces
publisher AIMS Press
series AIMS Mathematics
issn 2473-6988
publishDate 2021-03-01
description We present four versions of Egoroff's theorems for measurable closed-valued multifunctions on non-additive measure spaces. The conditions provided for each of these four versions are not only sufficient, but also necessary. In our discussions the continuity of non-additive measures is not required. The previous related results are improved and generalized.
topic random set
non-additive measure
the egoroff theorem
url http://www.aimspress.com/article/doi/10.3934/math.2021282?viewType=HTML
work_keys_str_mv AT taochen egoroffstheoremsforrandomsetsonnonadditivemeasurespaces
AT huizhang egoroffstheoremsforrandomsetsonnonadditivemeasurespaces
AT junli egoroffstheoremsforrandomsetsonnonadditivemeasurespaces
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