Research Article

The Borel property for 4-dimensional matrices

Volume: 45 Number: 2 April 1, 2016
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

  1. Borel E., Les probabilities denombrables et leurs applications arithmetiques, Rendiconti del Circolo Matematico di Palermo, 27, 247-271, 1909.
  2. Bromwich M.A., An introduction to the theory of infinite series, (Macmillan Co., London, 1942).
  3. 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.
  4. Crnjac M., Cunjalo F. and Miller H.I., ˘ Subsequence characterizations of statistical convergence of double sequences, Radovi Math., 12, 163-175, 2004.
  5. Garreau G.A., A note on the summation of sequences of 0’s and 1’s, Annals of Mathematics, 54, 183-185, 1951.
  6. Hill J.D., Summability of sequences of 0’s and 1’s, Annals of Mathematics, 46, 556-562, 1945.
  7. Hill J.D., The Borel property of summability methods, Pacific J. Math., 1, 399-409, 1951.
  8. 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

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