Let $\mu$ be the lebesgue measure and $f:\mathbb{R}^n \rightarrow \mathbb{R}^m$. When is true that $\mu (f(A)) \leq \mu (A)$?

Question

Let $\mu$ be the lebesgue measure. Let $A \subset \mathbb{R}^n$ and $f:\mathbb{R}^n \rightarrow \mathbb{R}^m$. I want to know the minimum conditions for when is true that $\mu (f(A)) \leq \mu (A)$. I began recently with measure study and i don´t know if there exist some theorem about this neither its conditions. Apparently yes, but what is its proof? If someone can give me a hand I would be very grateful. The special case I'm working with is taking compact $A$ and $f$ is $C^1$ with $m>n$.