6533b7d2fe1ef96bd125ea9b

RESEARCH PRODUCT

Existence of doubling measures via generalised nested cubes

Tapio RajalaAntti KäenmäkiVille SuomalaVille Suomala

subject

Applied MathematicsGeneral MathematicsDyadic cubesStructure (category theory)Space (mathematics)Measure (mathematics)CombinatoricsMetric spacePacking dimension28C15 (Primary) 54E50 (Secondary)Mathematics - Classical Analysis and ODEsSimple (abstract algebra)Classical Analysis and ODEs (math.CA)FOS: MathematicsUltrametric spaceMathematics

description

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 $\epsilon$.

yearjournalcountryeditionlanguage
2012-09-01Proceedings of the American Mathematical Society
https://doi.org/10.1090/s0002-9939-2012-11161-x