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Dimension function

In mathematics, the notion of an (exact) dimension function (also known as a gauge function) is a tool in the study of fractals and other subsets of metric spaces. Dimension functions are a generalisation of the simple "diameter to the dimension" power law used in the construction of s-dimensional Hausdorff measure.

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Dimension function

Nodes18
Edges17
Triples26
Avg. degree1.89
Density0.111111
Components1

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Dimension function

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related to References · 15
Dimension function → Cambridge, Cambridge Mathematical Library, Cambridge University Press, Cantor, Hausdorff, ISBN, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Nonlinearity, Olsen, Rogers, The, Third, Wikisource-logo
related to Example · 8
Dimension function → Almost, Brownian, Euclidean, For Brownian, Hausdorff, R2, Rn, The
related to Packing dimension · 3
Dimension function → Hausdorff, Just, Packing

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Important terminology

dimension hausdorff function measure exact diameter functions s-dimensional one metric μs euclidean finite strictly positive brownian gauge packing example volume

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SubjectPredicateObjectConfidenceSrc
Dimension functionrelated to ExampleAlmost0.60section
Dimension functionrelated to ExampleBrownian0.60section
Dimension functionrelated to ExampleEuclidean0.60section
Dimension functionrelated to ExampleHausdorff0.60section
Dimension functionrelated to ExampleThe0.60section
Dimension functionrelated to ExampleR20.60section
Dimension functionrelated to ExampleFor Brownian0.60section
Dimension functionrelated to ExampleRn0.60section
Dimension functionrelated to Packing dimensionPacking0.60section
Dimension functionrelated to Packing dimensionHausdorff0.60section
Dimension functionrelated to Packing dimensionJust0.60section
Dimension functionrelated to ReferencesLock-green0.60section

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