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I have always liked Volterra's functionthat has a derivative that everywhere which is bounded, discontinuous, and cannot be Riemann-integrated. It depends on the Cantor sets, of course, already mentioned. http://en.wikipedia.org/wiki/Volterra%27s_function I think it is probably in the book Possible reference: Bernard R. Gelbaum, John M. H. Olmsted: Counterexamples in Analysis. See also : http://en.wikipedia.org/wiki/CounterexampleMO:Integrability of derivatives. |
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I have always liked Volterra's function that has a derivative that cannot be Riemann-integrated. It depends on the Cantor sets, of course, already mentioned. http://en.wikipedia.org/wiki/Volterra%27s_function I think it is probably in the book: Bernard R. Gelbaum, John M. H. Olmsted: Counterexamples in Analysis. See also: |
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