Let $\Omega$ be an open bounded domain and $f:\mathbb{R}\to\mathbb{R}$ be a continuous and bounded from below function.
It is true that a positive constant $C$ exists such that
$$\int_{\Omega} f(t) dt\geq C?$$
I think it is true, but how to prove it?
Could anyone please help?
Thank you in advance!
Best Answer
No. Consider $f(x)=0$ on $x\in(0,1)$.
If you have a negative lower bound, cancellation could happen.
But if you have $f\ge 0$ (and continuous), then $\int_\Omega f>0$ if $f$ is not constantly zero.