Examples 7.1.9(c):

Is the Dirichlet function Riemann integrable on the interval [0, 1] ?
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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) = 0
Therefore, the Dirichlet function is not integrable over the interval [0, 1].

Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007