Research Article
Year 2016,
Volume: 45 Issue: 2, 473 - 482, 01.04.2016
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.
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.
- Móricz F. and Rhoades B.E., Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Phil. Soc. 104, 283-294, 1988
- Parameswaran M.R., Note on the summability of sequences of zeros and ones, Proc. Nat. Inst. Sci. India Part A 27, 129-136, 1961.
- Pringsheim A., On the theory of double infinite sequences of numbers. (Zur theorie der zweifach unendlichen zahlenfolgen.), Math. Ann., 53, 289-321, 1900.
- Robison G.M., Divergent double sequences and series, Trans. Amer. Math. Soc. 28, 50-73, 1926.
- Tas E. and Orhan C., Cesàro means of subsequences of double sequences, submitted. 482
- Visser C., The law of nought-or-one in the theory of probability, Studia Mathematica, 7, 143-149, 1938.
Year 2016,
Volume: 45 Issue: 2, 473 - 482, 01.04.2016
Abstract
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.
- Móricz F. and Rhoades B.E., Almost convergence of double sequences and strong regularity of summability matrices, Math. Proc. Camb. Phil. Soc. 104, 283-294, 1988
- Parameswaran M.R., Note on the summability of sequences of zeros and ones, Proc. Nat. Inst. Sci. India Part A 27, 129-136, 1961.
- Pringsheim A., On the theory of double infinite sequences of numbers. (Zur theorie der zweifach unendlichen zahlenfolgen.), Math. Ann., 53, 289-321, 1900.
- Robison G.M., Divergent double sequences and series, Trans. Amer. Math. Soc. 28, 50-73, 1926.
- Tas E. and Orhan C., Cesàro means of subsequences of double sequences, submitted. 482
- Visser C., The law of nought-or-one in the theory of probability, Studia Mathematica, 7, 143-149, 1938.
There are 14 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | April 1, 2016 |
| Published in Issue | Year 2016 Volume: 45 Issue: 2 |