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In page Riemann integral:
"The Lebesgue–Vitali theorem does not imply that all type of discontinuities have the same weight on the obstruction that a real-valued bounded function be Riemann integrable on [a, b]. In fact, certain discontinuities have absolutely no role on the Riemann integrability of the function—a consequence of the classification of the discontinuities of a function.[citation needed]
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