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Continuity of the integral function

The proof is a simple consequence of the mean value thoerem. If img, consider a point d. We have: img, where  is a number between the inf and the sup of f in [d,x] (or [x,d]). Then as x tends towards d, the last member tends to zero (due to the fact that f is bounded). This proves continuity of F.

first published on january 07 2003 - last updated on september 01 2003