2
votes
1answer
209 views

Lebesgue-integrable function

I have to decice if the following function is Lebesgue-integrable on $[0,1]$: $$g(x)=\frac{1}x\cos\left(\frac{1}x\right) $$ where $x\in[0,1]$.
0
votes
3answers
224 views

Lebesgue- integrability of roots and powers of a function

If the powers of a function $f$ are Lebesgue integrable what can we say about the original function? for example if we take $f=\frac{1}{x} on [1, \infty] $, it is not integrable but $f^2$ is. Is there ...