You always see in books that one advantage of the Lebesgue integral over the Riemann integral is that a sequence of continuous functions f_n does not have to converge unifomly to a function f to have:(adsbygoogle = window.adsbygoogle || []).push({});

integral of the limit of the sequence = the limit of the integrals of functions in the sequence

Can anybody give me an example where this equality fails using the Riemann integral, and does not fail using the Lebesgue integral?

Thank you

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# Lebesgue integral over the Riemann integral

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