Hausdorff dimension

English Etymology Introduced in 1918 by mathematician Felix Hausdorff. Noun en analysis 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. Hypernyms en fractal dimension Translations type of fractal dimension Chinese: Mandarin: cmn 豪斯多夫維數 Háosīduōfū wéishù Czech: cs Hausdorffova dimenze Finnish: fi Hausdorffin dimensio French: fr dimension de Hausdorff f Greek: el διάσταση Χάουσντορφ f Japanese: ja ハウスドルフ次元 Hausudorufu jigen Korean: ko 하우스도르프 차원 Russian: ru разме́рность Хаусдорфа f Spanish: es dimensión de Hausdorff f en eponyms en Fractals