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This is one exercise from Rudin's book,

Construct a continuous monotone function $f$ on $\mathbb{R}^1$ that is not constant on any segment but $f'(x)=0$ a.e.

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    Pardon my ignorance, what does a.e mean?2012-11-29
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    @ArmenTsirunyan https://en.wikipedia.org/wiki/Almost_everywhere2012-11-29
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    @kahen: Ah, OK, thanks :)2012-11-29
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    Devil's staircase?2012-11-29
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    @HagenvonEitzen the Cantor function doesn't quite work. It's constant on quite a few intervals.2012-11-29
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    As usual, Gelbaum and Olmsted's *Counterexamples in Analysis* proves to be a treasure. [Example 8.30](http://books.google.com/books?id=cDAMh5n4lkkC&pg=PA105&source=gbs_toc_r&cad=4#v=onepage&q&f=false) there will do the job.2012-11-29
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    Thanks! I am just going to ask the same question after one night's thinking...:(2013-01-09

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