A-Statistical Convergence of Subsequence of Double Sequences
Miller, Harry I.
Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 727-739 / Harvested from Biblioteca Digitale Italiana di Matematica
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The concept of statistical convergence of a sequence was first introduced by H. Fast [7] in 1951. Recently, in the literature, the concept of statistical convergence of double sequences has been studied. The main result in this paper is a theorem that gives meaning to the statement: s=si⁢j converges statistically A to L if and only if "most" of the "subsequences" of s converge to L in the ordinary sense. The results presented here are analogue of theorems in [12], [13] and [6] and are concerned with A statistical convergence, first introduced by Freedman and Sember [8]. Other related problems are considered.

Il concetto di convergenza statistica di una successione fu introdotto per la prima volta da H. Fast [7] nel 1951. Recentemente, nella letteratura è stato studiato il concetto di convergenza statistica di successioni doppie. Il risultato principale di questo lavoro è un teorema che dà significato all'affermazione: s=si⁢j converge A statisticamente a L se e solo se "la maggior parte" delle "sottosuccessioni" di s convergono a L nel senso ordinario. I risultati presentati qui sono l'analogo dei teoremi di [12], [13] e [6] e riguardano la convergenza A statistica introdotta per la prima volta da Freedman e Sember [8]. Vengono anche presi in considerazione altri problemi correlati.

Publié le : 2007-10-01
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     author = {Harry I. Miller},
     title = {A-Statistical Convergence of Subsequence of Double Sequences},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {727-739},
     zbl = {1139.40001},
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     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_727_0}
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Miller, Harry I. A-Statistical Convergence of Subsequence of Double Sequences. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 727-739. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_727_0/

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