If f is integrable on an interval [a,a+T] of length T,then prove that f is also integrable on any other interval [b,b+T] of length T.

Asked Oct 26 '18 at 12:49

Active Oct 26 '18 at 13:59

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If I can show that the function is integrable on any other interval of length T,I can certainly show that the integration values of that function over these two different intervals of same length are equal. That part is pretty easy. How to show that f is integrable on any other interval of same length?

edited Oct 26 '18 at 13:59

asked Oct 26 '18 at 12:49

ARKAPROVO CHAKARBORTY

Don't you see anything wrong with the question from the title? Besides, what has this to do with fourier-series? – José Carlos Santos Oct 26 '18 at 12:51
Yeah I can change the Tag...but the question is completely okay. – ARKAPROVO CHAKARBORTY Oct 26 '18 at 12:57
The question is as if you were asking: If $A$ is a set of real numbers and if every $B\subset A$ is bounded, then prove that every $C\subset A$ is bounded. – José Carlos Santos Oct 26 '18 at 13:00
No...my question isn't indicating that. I said "If f is integrable on any interval [a,a+T]..."...here it doesn't mean that f is integrable on any interval of length T...yeah I'm choosing one interval arbitrarily...but once I've chosen one interval,it is fixed...like this interval should be a concrete one and given in the question. – ARKAPROVO CHAKARBORTY Oct 26 '18 at 13:09
Okay...for convenience,I've made a change to my question. I think now my question is understandable! – ARKAPROVO CHAKARBORTY Oct 26 '18 at 13:17
My guess is that you also forgot to mention that $T$ is a period of $f$. – José Carlos Santos Oct 26 '18 at 13:19

If f is integrable on an interval [a,a+T] of length T,then prove that f is also integrable on any other interval [b,b+T] of length T.

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