Hausdorff dimension en · NOUN
Etymology
Introduced in 1918 by mathematician Felix Hausdorff.
Meanings
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A type of fractal dimension, a real-valued measure of a geometric object that assigns 1 to a line segment, 2 to a square and 3 to a cube. Formally, given a metric space X and a subset of X labeled S, the Hausdorff dimension of S is the infimum of all real-valued d for which the d-dimensional Hausdorff content of S is zero.
If S is nonempty then if the d-dimensional Hausdorff content of S is zero then d is larger than the Hausdorff dimension of S, and if the d-dimensional Hausdorff content of S is infinite then d is smaller or equal to the Hausdorff dimension of S. If the d-dimensional Hausdorff content of S is finite and positive then d is equal to the Hausdorff dimension of S.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Hausdorff dimensions | Number=Plur | lexicographic |
Hypernyms
Translations (9)
fi Hausdorffin dimensio (type of fractal dimension) · ko 하우스도르프 차원 (type of fractal dimension) · fr dimension de Hausdorff (type of fractal dimension) · ru разме́рность Хаусдорфа (type of fractal dimension) · ja ハウスドルフ次元 (type of fractal dimension) · cmn 豪斯多夫維數 /豪斯多夫维数 (type of fractal dimension) · es dimensión de Hausdorff (type of fractal dimension) · el διάσταση Χάουσντορφ (type of fractal dimension) · cs Hausdorffova dimenze (type of fractal dimension)