On partial limits of sequences

Kód výsledku v 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>
Výsledek na webu
<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>

Jazyk výsledku
angličtina
Název v původním jazyce
On partial limits of sequences
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
On partial limits of sequences
Popis výsledku anglicky
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.

Projekt
<a href="/cs/project/GA17-02804S" target="_blank" >GA17-02804S: Vlastnosti číselných posloupností a jejich aplikace</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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