Document Type


Publication Date



Eberly College of Arts and Sciences




We present a simple argument that for every continuous function f : R → R its restriction to some perfect set is Lipschitz. We will use this result to provide an elementary proof of the C 1 free interpolation theorem, that for every continuous function f : R → R there exists a continuously differentiable function g : R → R which agrees with f on an uncountable set. The key novelty of our presentation is that no part of it, including the cited results, requires from the reader any prior familiarity with the Lebesgue measure theory.

Included in

Mathematics Commons


To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.