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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'fundamental theorems of calculus for Lebesgue integration'
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integrability is for free by paolini
Correction id: 2168
Filed on: 2003-07-15 11:07:34
Status: Accepted on 2004-02-27 11:54:22
Type: Addendum
Correction text:
About the second statement:
You assume that $f$ is integrable on $[0,x]$. I suppose you meant $[c,x]$ instead of $[0,x]$. Anyway this hypothesys is not needed since a continuous function is integrable on every closed and bounded interval.
About the first statement:
Are you sure of this result? I think that (if true) it is not trivial at all. You should prove that $F'(x)$ is integrable also when it is not continuous. I think that here it would be nice to suppose that $F'$ is integrable "a priori"...
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No comment from object owner mathcam.
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