The characteristic function of the RATIONALS is a well-known example of a bounded function that is not Riemann integrable. But is the characteristic function of the IRRATIONALS (that is, the function that is 1 at every irrational number and 0 at every rational number) Riemann integrable on an arbitrary interval [a,b]? It seems like it would be, and that its integral would be equal to 1.(adsbygoogle = window.adsbygoogle || []).push({});

But maybe I'm wrong. Anyone know for a fact?

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# Is the characteristic function of the irrationals Riemann integrable on [a,b]?

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