I have problem with the exercise that follows.
Let $(z_m)_m \in R^n$ so that $\Vert z_m \Vert \rightarrow \infty$ when $m\to \infty$. Let $f:R^n \rightarrow [-\infty;+\infty]$ integrable.
Show that if $K \subset R^n$ is a compact $\lim_{m\rightarrow\infty} \int_{z_m+K}f d\lambda=0$.
I manage to find the result for $\vert f \vert$. But I can find a way to get to result for f, as asked in the exercise.I thought about using the result for $\vert f \vert$ but then I stuck..so maybe there's another way If someone can help me.
Update:
Also because then I've another problem related to the first one and I found a way to show it related to the exercise before with $\vert f \vert$ instead of $f$.But maybe there's a better way to show it.