If f(x) is integrable on [a,b], let g(x)=min(f(x),10). Is g(x) integrable on [a,b]? (Prove or find a counterexample.)

Asked Jan 13 '19 at 00:51

Active Jan 13 '19 at 01:02

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Any hint? I am thinking about the trignometric function as a counterexample, but I still cannot have a clue.

asked Jan 13 '19 at 00:51

RayHH13

1

Please see this post: https://math.stackexchange.com/questions/86031/if-f-and-g-integrable-then-max-f-g-is. – Hung Hua Jan 13 '19 at 01:08
If the integrals are in Lebesgue sense then the answer is YES. – Kavi Rama Murthy Jan 13 '19 at 04:59

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