Existence of doubling measures via generalised nested cubes

By A. Kaenmaki, T. Rajala, Ville Suomala. 2010

88 citations recorded by the source corpus.

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 $\epsilon$.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c97f87f50643a8fe6bf1915248586536db1627e1

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In Mathematical Physics

Citations in the corpus

Systems of dyadic cubes in a doubling metric space (2010, background): “-open and closed cubes. While this may not be the absolute shortest route to the half-open cubes alone (for which one should probably consult the recent paper of A. Käenmäki, T. Rajala and V. Suomala [14]), we ﬁnd the properties of the open and closed cubes proven on the way to be useful as well. Th”
Dimensions, Whitney covers, and tubular neighborhoods (2012, background): “The reverse implication is true if X is assumed to be complete; see [38, 39, 26, 43, 7, 19].”