Let $V$ be a real vector space of finite dimension $n$ endowed with an invariant measure $\mu$. Let $\Gamma$ be a lattice in $V$. I wonder how and why $\mu$ induces a finite measure on $V/\Gamma$.
This is from Serre's a course in arithmetic, page 106-107.
I understand that if $V:=\mathbb R^n$ and $\mu$ is the Lebesgue measure then $\mathbb R^n/ \Gamma$ is a high dimensional torus whose measure should be identified with the measure of a fundamental domain in $\mathbb R^n$.
However, here $\mu$ is just an invariant measure (invariant to translation I guess) and I have no idea how $\mu$ descends to a finite measure on $V/\Gamma$.