7.4. Lebesgue Integral

Example 7.4.7(b): Riemann implies Lebesgue Integrable

Show that the converse of the above theorem is false, i.e. not every bounded Lebesgue integrable function is Riemann integrable.
The Dirichlet function restricted to [0, 1] is bounded and Lebesgue integrable (with the intgral zero), while it is not Riemann integrable.
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