On partial limits of sequences

Autor: János T. Tóth, Ladislav Mišík
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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