On partial limits of sequences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA200212F" target="_blank" >RIV/61988987:17310/19:A200212F - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/abs/pii/S0165011419301083" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0165011419301083</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2019.01.013" target="_blank" >10.1016/j.fss.2019.01.013</a>

Result language
angličtina
Original language name
On partial limits of sequences
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-02804S" target="_blank" >GA17-02804S: Properties of number sequences and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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