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Dimension of the graph of Riemann integrable functions


Author: James Foran
Journal: Proc. Amer. Math. Soc. 104 (1988), 219-220
MSC: Primary 28A75; Secondary 26A42
DOI: https://doi.org/10.1090/S0002-9939-1988-0958070-2
MathSciNet review: 958070
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Abstract: The Hausdorff $ h - m$ measure of the graph of a Riemann integrable function is shown to be finite provided $ h$ satisfies an inequality related to the rate of convergence of the upper and lower Riemann sums.


References [Enhancements On Off] (What's this?)

  • [1] A. S. Besicovitch and H. D. Ursell, Sets of fractional dimension, V: On dimensional numbers of some continuous curves, J. London Math. Soc. (2) 32 (1937), 142-153.
  • [2] R. Daniel Mauldin and S. C. Williams, On the Hausdorff dimension of some graphs, Trans. Amer. Math. Soc. 298 (1986), 793-803. MR 860394 (88c:28006)
  • [3] C. A. Rogers, Hausdorff measures, Cambridge Univ. Press, 1970. MR 0281862 (43:7576)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0958070-2
Keywords: Hausdorff measure, Riemann integral
Article copyright: © Copyright 1988 American Mathematical Society

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