EN
The Borel property for 4-dimensional matrices
Abstract
In 1909 Borel has proved that “Almost all of the sequences of 0’s and 1’s
are Cesàro summable to 1
2
". Then Hill has generalized Borel’s result
to two dimensional matrices. In this paper we investigate the Borel
property for 4-dimensional matrices.
Keywords
References
- Borel E., Les probabilities denombrables et leurs applications arithmetiques, Rendiconti del Circolo Matematico di Palermo, 27, 247-271, 1909.
- Bromwich M.A., An introduction to the theory of infinite series, (Macmillan Co., London, 1942).
- Connor J., Almost none of the sequences of 0’s and 1’s are almost convergent, Internat. J. Math. Math. Sci. 13, 775-777, 1990.
- Crnjac M., Cunjalo F. and Miller H.I., ˘ Subsequence characterizations of statistical convergence of double sequences, Radovi Math., 12, 163-175, 2004.
- Garreau G.A., A note on the summation of sequences of 0’s and 1’s, Annals of Mathematics, 54, 183-185, 1951.
- Hill J.D., Summability of sequences of 0’s and 1’s, Annals of Mathematics, 46, 556-562, 1945.
- Hill J.D., The Borel property of summability methods, Pacific J. Math., 1, 399-409, 1951.
- Hill J.D., Remarks on the Borel property, Pacific J. Math., 4, 227-242, 1954.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Publication Date
April 1, 2016
Submission Date
December 25, 2014
Acceptance Date
March 30, 2015
Published in Issue
Year 2016 Volume: 45 Number: 2
APA
Taş, E. (2016). The Borel property for 4-dimensional matrices. Hacettepe Journal of Mathematics and Statistics, 45(2), 473-482. https://izlik.org/JA47RA72DX
AMA
1.Taş E. The Borel property for 4-dimensional matrices. Hacettepe Journal of Mathematics and Statistics. 2016;45(2):473-482. https://izlik.org/JA47RA72DX
Chicago
Taş, Emre. 2016. “The Borel Property for 4-Dimensional Matrices”. Hacettepe Journal of Mathematics and Statistics 45 (2): 473-82. https://izlik.org/JA47RA72DX.
EndNote
Taş E (April 1, 2016) The Borel property for 4-dimensional matrices. Hacettepe Journal of Mathematics and Statistics 45 2 473–482.
IEEE
[1]E. Taş, “The Borel property for 4-dimensional matrices”, Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 2, pp. 473–482, Apr. 2016, [Online]. Available: https://izlik.org/JA47RA72DX
ISNAD
Taş, Emre. “The Borel Property for 4-Dimensional Matrices”. Hacettepe Journal of Mathematics and Statistics 45/2 (April 1, 2016): 473-482. https://izlik.org/JA47RA72DX.
JAMA
1.Taş E. The Borel property for 4-dimensional matrices. Hacettepe Journal of Mathematics and Statistics. 2016;45:473–482.
MLA
Taş, Emre. “The Borel Property for 4-Dimensional Matrices”. Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 2, Apr. 2016, pp. 473-82, https://izlik.org/JA47RA72DX.
Vancouver
1.Emre Taş. The Borel property for 4-dimensional matrices. Hacettepe Journal of Mathematics and Statistics [Internet]. 2016 Apr. 1;45(2):473-82. Available from: https://izlik.org/JA47RA72DX