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Question: suppose g c r is an open set in 01...

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Suppose G C R is an open set in [0,1] containing rational points and such that m (G) < 1/2. (Why does such set exist?) Prove that the characteristic function of G, is not Riemann integrable of [0, 1 Note that unlike Dirichelet function, we cannot modify xG on a set of measure zero to obtain a Riemann integrable function, i.e. it is, in terms of measure, substantially different from any Riemann integrable function.

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