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Dimension of a measure

2000; Polish Academy of Sciences; Volume: 142; Issue: 3 Linguagem: Inglês

10.4064/sm-142-3-219-233

1730-6337

Pertti Mattila, Manuel Morán, José-Manuel Rey,

Advanced Differential Equations and Dynamical Systems

We propose a framework to define dimensions of Borel measures in a metric space by formulating a set of natural properties for a measure-dimension mapping, namely monotonicity, bi-Lipschitz invariance, (σ-)stability, etc. We study the behaviour of most po