TITLE: Important examples of measures which are not $\sigma$-finite
QUESTION [12 upvotes]: I think a measure which is not $\sigma$-finite is pain in the ass.
I wish I could safely assume all the measures are $\sigma$-finite.
I wonder if my wish is reasonable.
Here's my question:
what are important examples of measures which are not $\sigma$-finite?
Of course, "important" is a subjective word. So this is a soft question.
This is also a big-list question.

REPLY [9 votes]: I believe the most important class of non-$\sigma$-finite measures is provided by the Hausdorff measures.
$\mathcal{H}_{\alpha}$ on $\mathbb{R}^d$ where $d > \alpha$ is not $\sigma$-finite. (Because any subset of finite $\mathcal{H}_{\alpha} $ measure is of null Lebesgue measure)