Existence of doubling measures via generalised nested cubes
Classical Analysis and ODEs
2017-02-03 v2
Abstract
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 there is a doubling measure having full measure on a set of packing dimension at most .
Cite
@article{arxiv.1011.0683,
title = {Existence of doubling measures via generalised nested cubes},
author = {Antti Käenmäki and Tapio Rajala and Ville Suomala},
journal= {arXiv preprint arXiv:1011.0683},
year = {2017}
}