Appert space

Some time ago, I was wondering about the various definitions of a Radon measure, and in particular about the relation between local finiteness and the requirement that the measure of every compact subset be finite. (I will explain everything.) The former implies the latter, but what about the latter? It turns out that the two are not equivalent, and this will be a convenient excuse to introduce a simple counterexample, due to Antoine Appert in 1934, for different reasons. Read the full post.