Existence of doubling measures via generalised nested cubes

Käenmäki, Antti; Rajala, Tapio; Suomala, Ville

doi:10.1090/S0002-9939-2012-11161-X

Existence of doubling measures via generalised nested cubes
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by Antti Käenmäki, Tapio Rajala and Ville Suomala PDF

Proc. Amer. Math. Soc. 140 (2012), 3275-3281 Request permission

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 $\varepsilon >0$ there is a doubling measure having full measure on a set of packing dimension at most $\varepsilon$.

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