  Working on doubling metric spaces, we construct generalised dyadic cubes
adapting ultrametric structure. If the space is complete, then the existence of
such cubes and the mass distribution principle lead into a simple proof for the
existence of doubling measures. As an application, we show that for each
$\epsilon>0$ there is a doubling measure having full measure on a set of
packing dimension at most $\epsilon$.

Classical Analysis and ODEs