Search results for " 54E50"

showing 2 items of 2 documents

Existence of doubling measures via generalised nested cubes

2012

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 $\epsilon$.

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 spaceMathematicsProceedings of the American Mathematical Society
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Local multifractal analysis in metric spaces

2013

We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild regularity conditions. On the other hand, we consider a local spectrum that can be used to gain finer information on the local behaviour of measures than its global counterpart.

Pure mathematicsApplied MathematicsGeneral Physics and AstronomyMetric Geometry (math.MG)Statistical and Nonlinear PhysicsDynamical Systems (math.DS)Multifractal systemType (model theory)28A80 28D20 54E50Metric spaceLocal spectrumMathematics - Metric GeometryMathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics - Dynamical SystemsMathematical PhysicsMathematicsNonlinearity
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