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On Nörlund summability of random variables to zero


Author: George E. Forsythe
Journal: Bull. Amer. Math. Soc. 53 (1947), 302-313
DOI: https://doi.org/10.1090/S0002-9904-1947-08788-7
MathSciNet review: 0020738
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References [Enhancements On Off] (What's this?)

  • 1. G. E. Forsythe, Cesàro summability of independent random variables, Duke Math. J. vol. 10 (1943) pp. 397-428. MR 8656
  • 2. E. Hille and J. D. Tamarkin, On the summability of Fourier series. I, Trans. Amer. Math. Soc. vol. 34 (1932) pp. 757-783. MR 1501662
  • 3. Th. Kaluza, Ueber die Koeffizienten reziproker Potenzreihen, Math. Zeit. vol. 28 (1928) pp. 161-170; p. 162. MR 1544949
  • 4. T. Kojima, On generalized Toeplitz's theorems on limit and their applications, Tôhoku Math. J. vol. 12 (1917) pp. 291-326; p. 300.
  • 5. P. Lévy, Sur la sommabilité des séries aléatoires divergentes, Bull. Soc. Math. France vol. 63 (1935) pp. 1-35. MR 1505029
  • 6. N. E. Nörlund, Sur une application des fonctions permutables, Lunds Universitets Årsskrift, Afdelning 2, N. S. vol. 16 (1920); 10 pp.
  • 7. M. Riesz, Sur l'équivalence de certaines méthodes de sommation, Proc. London Math. Soc. (2) vol. 22 (1923-1924) pp. 412-419.
  • 8. L. L. Silverman and J. D. Tamarkin, On the generalization of Abel's theorem for certain definitions of summability, Math. Zeit. vol. 29 (1929) pp. 161-170. MR 1544999
  • 9. G. F. Woronoi, Extension of the notion of the limit of the sum of an infinite series, translated and discussed by J. D. Tamarkin, Ann. of Math. (2) vol. 33 (1932) pp. 422-428. MR 1503066


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1947-08788-7

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