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HAUSDORFF-BESICOVITCH MEASURE [1 record]

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Record 1 1989-12-18

English

Subject field(s)
  • Mathematics
  • Computer Graphics
DEF

A non-zero but finite s-dimensional Hausdorff measure.

OBS

A fractal measure devised in 1935 by Besicovitch based on Felix Hausdorff's work (1919) on non-integer dimensions for geometrically very complex objects. See fractional dimension, fractal dimension, Hausdorff dimension.

French

Domaine(s)
  • Mathématiques
  • Infographie
CONT

Dans le contexte triadique de Cantor, partons d'une masse distribuée sur (0,1) avec la densité uniforme égale à 1. Effacer le tiers central divise cette masse en parties égales .. réparties avec les densités 3/2, o, et 3/2 [...] Quand on aura répété la procédure à l'infini, la masse formera ce que nous allons appeler une mesure de Besicovitch [...] Il est clair, pour commencer, qu'aucun intervalle ouvert ne constitue une intermission absolue.

Spanish

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