I recently watched some measure theory lectures online. They didn't post lecture notes and I can't find which video exactly it was.
I think there was a theorem that goes something along the lines of:
If $f:\mathbb{R^N} \to \mathbb{R^N}$ is Lipshitz with Lipschitz constant $L$, and $\lambda$ stands for Lebesgue measure, then $\lambda(f(A)) \leq L\lambda(A)$ for $A$ measurable.
Is this correct, or is there a similar looking theorem that I might be thinking of? Thanks.
Best Answer
Just posting this in case others search for it later. As @Leonid mentioned, here is the theorem from Geometry of sets and measures in Euclidean spaces by Pertti Mattila: