Talk:Absolute continuity
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Is there an example of a uniformly continuous function that is not absolutely continous? Albmont 17:43, 2 January 2007 (UTC)
- Yes. The Cantor function, when restricted to the compact interval [0, 1], is a continuous function defined on a compact set, and is therefore uniformly continuous. However, is it not absolutely continuous, as the Cantor distribution is not absolutely continuous with respect to Lebesgue measure. Sullivan.t.j 18:10, 2 January 2007 (UTC)
