# A-Statistical Convergence of Subsequence of Double Sequences

• Volume: 10-B, Issue: 3, page 727-739
• ISSN: 0392-4041

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## Abstract

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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: $s={s_{ij}}$ 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.

## How to cite

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Miller, Harry I.. "A-Statistical Convergence of Subsequence of Double Sequences." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 727-739. <http://eudml.org/doc/290396>.

@article{Miller2007,
abstract = {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: $s=\{s_\{ij\}\}$ 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.},
author = {Miller, Harry I.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {727-739},
publisher = {Unione Matematica Italiana},
title = {A-Statistical Convergence of Subsequence of Double Sequences},
url = {http://eudml.org/doc/290396},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Miller, Harry I.
TI - A-Statistical Convergence of Subsequence of Double Sequences
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 727
EP - 739
AB - 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: $s={s_{ij}}$ 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.
LA - eng
UR - http://eudml.org/doc/290396
ER -

## References

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1. BILLINGSLEY, P., Probability and Measure, Third Edition, Wiley and Sons, 1995. MR1324786
2. BUCK, R. C., Generalized asymptotic density, Amer. J. Math., 74 (1953), 334-346. Zbl0050.05901MR54000DOI10.2307/2372456
3. CONNOR, J., The statistical and strong p-Cesáro convergence of sequences, Analysis, 8 (1988), 47-63. Zbl0653.40001MR954458
4. CONNOR, J., Almost none of the sequences of 0's and 1's are almost convergent, Int. J. Math. Math. Sci., 13 (1990), 775-778. Zbl0717.40002MR1078343DOI10.1155/S0161171290001077
5. CONNOR, J., Two valued measure and summability, Analysis, 10 (1990), 373-385. Zbl0726.40009MR1085803DOI10.1524/anly.1990.10.4.373
6. CRNJAC, M. - CUNJALO, F. - MILLER, H. I., Subsequence characterizations of statistical convergence of double sequences, Rad. Mat., 12 (2) (2004), 163-175. Zbl1066.40002MR2065556
7. FAST, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244. Zbl0044.33605MR48548
8. FREEDMAN, A. R. - SEMBER, J. J., Densities and summability, Pacific J. Math., 95 (1981), 293-305. Zbl0504.40002MR632187
9. FRIDY, J., On statistical convergence, Analysis, 5 (1985), 301-313. Zbl0588.40001MR816582DOI10.1524/anly.1985.5.4.301
10. FRIDY, J. - ORHAN, C., Lacunary statistical convergence, Pacific J. Math., 160 (1993), 43-51. Zbl0794.60012MR1227502
11. FRIDY, J. - ORHAN, C., Lacunary statistical summability, J. Math. Anal. Appl., 173 (1993). Zbl0786.40004MR1209334DOI10.1006/jmaa.1993.1082
12. MILLER, H. I., Measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347 (5) (1995), 1811-1819. Zbl0830.40002MR1260176DOI10.2307/2154976
13. MILLER, H. I. - ORHAN, C., On almost convergent and statistically convergent subsequences, Acta Math. Hung., 93 (1-2) (2001), 135-151. Zbl0989.40002MR1924673DOI10.1023/A:1013877718406
14. MÓRICZ, F., Statistical convergence of multiple sequences, Arch. Math. (Basel), 81 (2003), 82-89. MR2002719DOI10.1007/s00013-003-0506-9

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