### A note on the dimension Dind

W. Kulpa (1972)

Colloquium Mathematicae

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W. Kulpa (1972)

Colloquium Mathematicae

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R. Duda (1979)

Colloquium Mathematicae

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R. Đorđević (1989)

Matematički Vesnik

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L. Polkowski (1985)

Colloquium Mathematicae

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Veerman, J.J.P., Stošić, B.D. (2000)

Experimental Mathematics

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Juan B. Sancho de Salas, M.ª Teresa Sancho de Salas (1988)

Extracta Mathematicae

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Herrmann Haase (1988)

Acta Universitatis Carolinae. Mathematica et Physica

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van Wamelen, Paul (1999)

Beiträge zur Algebra und Geometrie

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D. A. Moran (1976)

Colloquium Mathematicae

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Lu-ming Shen (2010)

Acta Arithmetica

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Józef Myjak, Ryszard Rudnicki (2007)

Bollettino dell'Unione Matematica Italiana

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A relationship between the information dimension and the average dimension of a measure is given. Properties of the average dimension are studied.

Yasunao Hattori (1987)

Fundamenta Mathematicae

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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.