## Theorem 7.4.7: Riemann implies Lebesgue Integrable |

If |

Since every step function is also a simple function, every upper sum
is a simple function that is bigger than *f*, and every lower
function is a simple function less than *f*. Therefore:

But ifI_{*}(f) I_{*}(f)_{L}I^{*}(f)_{L}I^{*}(f)