Dimension of the graph of Riemann integrable functions
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- by James Foran PDF
- Proc. Amer. Math. Soc. 104 (1988), 219-220 Request permission
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
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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.
- R. Daniel Mauldin and S. C. Williams, On the Hausdorff dimension of some graphs, Trans. Amer. Math. Soc. 298 (1986), no. 2, 793–803. MR 860394, DOI 10.1090/S0002-9947-1986-0860394-7
- C. A. Rogers, Hausdorff measures, Cambridge University Press, London-New York, 1970. MR 0281862
Additional Information
- © Copyright 1988 American Mathematical Society
- 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