Dimension of measures
Herrmann Haase (1990)
Acta Universitatis Carolinae. Mathematica et Physica
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Herrmann Haase (1990)
Acta Universitatis Carolinae. Mathematica et Physica
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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.
Herrmann Haase (1988)
Acta Universitatis Carolinae. Mathematica et Physica
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M. Charalambous (1976)
Fundamenta Mathematicae
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Roman Sikorski (1951)
Fundamenta Mathematicae
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Alois Švec (1968)
Czechoslovak Mathematical Journal
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