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Proceedings of the American Mathematical Society

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An arithmetic property of Riemann sums


Author: Walter Rudin
Journal: Proc. Amer. Math. Soc. 15 (1964), 321-324
MSC: Primary 26.46; Secondary 28.00
DOI: https://doi.org/10.1090/S0002-9939-1964-0159918-8
MathSciNet review: 0159918
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References [Enhancements On Off] (What's this?)

  • [1] B. Jessen, On the approximation of Lebesgue integrals by Riemann sums, Ann. of Math. (2) 35 (1934), no. 2, 248–251. MR 1503159, https://doi.org/10.2307/1968429
  • [2] R. Salem, Sur les sommes Riemanniennes des fonctions sommables, Mat. Tidsskr. B. 1948 (1948), 60–62 (French). MR 0027827
  • [3] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
  • [4] J. Marcinkiewicz and A. Zygmund, Mean values of trigonometrical polynomials, Fund. Math. 28 (1937), 131-166.
  • [5] H. D. Ursell, On the behaviour of a certain sequence of functions derived from a given one, J. London Math. Soc. 12 (1937), 229-232.

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DOI: https://doi.org/10.1090/S0002-9939-1964-0159918-8
Article copyright: © Copyright 1964 American Mathematical Society