On partial limits of sequences

Limit of sequences is a basic concept in mathematical analysis. In this paper we study it in more details using another basic concept of analysis, measure on sets of positive integers. A key role in our considerations is played by the concept of a degree of convergence of a given sequence to a given...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 375; pp. 179 - 190
Main Authors Mišík, Ladislav, Tóth, János T.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.11.2019
Subjects
Convergence with respect to a measure
Degree of convergence
General measure
Limit of sequence
Metric space
Limit of sequence
Degree of convergence
Convergence with respect to a measure
Metric space
General measure
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Summary:Limit of sequences is a basic concept in mathematical analysis. In this paper we study it in more details using another basic concept of analysis, measure on sets of positive integers. A key role in our considerations is played by the concept of a degree of convergence of a given sequence to a given point with respect to a particular measure on the set of positive integers, as a number in interval [0,1]. We study its properties depending on properties of the chosen measure. It appears that standard limits and their known generalizations (convergence with respect to a filter or ideal) are extremal special cases in our approach.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2019.01.013