Looking for examples of doubling measures with references

Question

I am looking for examples of doubling measures apart from the Lebesgue measure on $\mathbb{R}^{d}.$ Furthermore, when is the Lebesgue measure restricted on a subset of $\mathbb{R}^{d}$ a doubling measure, or when is the volume measure on a Riemannian manifold, a doubling measure? Please provide some references. I found a lot of folklore but is quite hard to find specific references.

Answer 1

Hausdorff measure restricted to affine subspaces in $\mathbb{R}^n$ is an example.

The case of manifolds, you can consider spherical Hausdorff measure restricted to vertial homogeneus subgroups in the heisenberg group.

I do not think there is any need of a reference for these really simple examples.

Maybe if you esplain more what you need, rather than asking for non trivial examples with references, it may be easier to give a precise answer.