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math.CA2010★ 41 cited
Existence of doubling measures via generalised nested cubes
Antti Käenmäki, Tapio Rajala, Ville Suomala
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 dis…
math.CA2010★ 6 cited
Local homogeneity and dimensions of measures
Antti Käenmäki, Tapio Rajala, Ville Suomala
We introduce two new concepts, local homogeneity and local L^q-spectrum, both of which are tools that can be used in studying the local structure of measures. The main emphasis is…