From the definition of a doubling measure on wikipedia:
"A measure on a metric space X is said to be doubling if the measure of any ball is approximately the measure of its double, or more precisely, if there is a constant $C > 0$ such that
for all x in X and r > 0. In this case, we say μ is C-doubling.
A simple example of a doubling measure is Lebesgue measure on a Euclidean space"
This doesn't make sense to me. The description says that "the measure of any ball is approximately the measure of its double", but that doesn't seem to be true for the $2d$ Lebesgue measure, ie area.
I'm just confused and I have a limited understanding of measure theory. Could someone please clarify?