I'm working through a proof and one of the comments is that for a function $f\in L_p (\mathbb{T})$:
$\lim_{t\to 0}\;\|f(\cdot + t) - f\|_p = 0.$
How do I prove it? I think it is intuitively clear if $f$ is a step function, but what about for an arbitrary $p$ integrable function?