It is well known that if $f : [0;1] \to {\mathbb R}$ is a nondecreasing function, then the set $E$ of points where $f$ is not differentiable has Lebesgue measure zero. Is there an example where $E$ is not countable ? .
Differentiability of a monotone function
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real-analysis
measure-theory
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0Thanks for the references Dave. – 2012-03-29
2 Answers
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You could find a whole chapter devoted to this topic, with lots of examples and counterexamples in the book http://books.google.fr/books/about/A_first_course_in_Sobolev_spaces.html?id=W3RLWwnY0RkC&redir_esc=y