Existence of doubling measures via generalised nested cubes

Details Existence of doubling measures via generalised nested cubes Existence of doubling measures via generalised nested cubes

2010-11-02

arxiv.org/abs/1011.0683v2

Mathematics

Classical Analysis and ODEs

Scientific paper

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 $\epsilon$.

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