7.1. Riemann Integral
Is the Dirichlet function Riemann integrable on the interval [0, 1] ?In a previous example we have shown that U(f, P) = 1 and L(f, P) = 0, regardless of the partition. Therefore:
I*(f) = 1 and I*(f) = 0Therefore, the Dirichlet function is not integrable over the interval [0, 1].