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2011/2012 The Hausdorff Dimension of Graphs of Prevalent Continuous Functions
Jonathan M. Fraser, James T. Hyde
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Real Anal. Exchange 37(2): 333-352 (2011/2012).


We prove that the Hausdorff dimension of the graph of a prevalent continuous function is 2. We also indicate how our results can be extended to the space of continuous functions on \([0,1]^d\) for \(d \in \mathbb{N}\) and use this to obtain results on the ‘horizon problem’ for fractal surfaces. We begin with a survey of previous results on the dimension of a generic continuous function.


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Jonathan M. Fraser. James T. Hyde. "The Hausdorff Dimension of Graphs of Prevalent Continuous Functions." Real Anal. Exchange 37 (2) 333 - 352, 2011/2012.


Published: 2011/2012
First available in Project Euclid: 15 April 2013

zbMATH: 1275.28009
MathSciNet: MR3080596

Primary: 28A78 , 28A80
Secondary: 54E52

Keywords: Baire category , continuous functions , Hausdorff dimension , horizons , prevalence , typical

Rights: Copyright © 2011 Michigan State University Press

Vol.37 • No. 2 • 2011/2012
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