Abstract
We present an elementary proof that the graph of a continuous function from $\mathbb{R}$ to $\mathbb{R}$ is not purely unrectifiable. As a consequence of our method, we observe that all continuous functions from $\mathbb{R}$ to $\mathbb{R}$ meet the graph of some monotonic function in a set of positive linear measure.
Citation
Toby C. O’Neil. "Graphs of Continuous Functions from ℝ to ℝ Are Not Purely Unrectifiable." Real Anal. Exchange 26 (1) 445 - 448, 2000/2001.
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