On partial limits of sequences
Autor: | János T. Tóth, Ladislav Mišík |
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Rok vydání: | 2019 |
Předmět: | |
Zdroj: | Fuzzy Sets and Systems. 375:179-190 |
ISSN: | 0165-0114 |
DOI: | 10.1016/j.fss.2019.01.013 |
Popis: | 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. |
Databáze: | OpenAIRE |
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