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The proof is a simple consequence of the mean value thoerem. If
, consider a point *d*. We have: , 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*.

copyright 2000 et seq. maddalena falanga & luciano battaia

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