Displaying similar documents to “New inequalities on fractal analysis and their applications.”

Dimension of measures

Herrmann Haase (1990)

Acta Universitatis Carolinae. Mathematica et Physica

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Dimension of a measure

Pertti Mattila, Manuel Morán, José-Manuel Rey (2000)

Studia Mathematica

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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 popular definitions of measure dimensions in regard to our list, with special attention to the standard correlation dimensions and their modified versions.