## 7.4. Lebesgue Integral

### Example 7.4.9(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.