I'm trying to prove that subset X of space $\mathcal L^2(a,b)$ is precompact if and only if
$\forall \varepsilon>0$ $\exists \delta = \delta(\varepsilon)>0$ that $\forall$ $h, |h|<\delta$ and $x \in X$
$\int_a^b |x(t+h)-x(t)|^2 dt < \varepsilon$
how it can be done? i suppose it's true, anyways i also can't prove why it's not