TERMIUM Plus^®

Record 1,  Textual support,  English

Record number: 1, Textual support number: 1 CONT

The Hausdorff dimension, also called the Hausdorff-Besicovitch dimension in one of the possible dimensions.  4, record 1, English, - Hausdorff%20dimension

Record number: 1, Textual support number: 2 CONT

The Hausdorff dimension is defined for any subset of R [exponent]n that you can probably imagine. This includes all open sets, closed sets, countable unions of closed sets, countable intersections of open sets, etc. It will follow easily from the definition that Hausdorff dimension is not invariant under homeomorphisms. However, the topological dimension of E is the infimum of the Hausdorff dimensions of its homeomorphic images h(E). Later we will discover that Hausdorff dimension is invariant under something slightly stronger - quasi-isometries (sometimes called "bi-Lipschitz maps" or "Lipeomorphic maps"). Indeed, we will see that the equivalence class of quasi-isometric self-similar curves is completely determined by Hausdorff dimension!  5, record 1, English, - Hausdorff%20dimension

Record 1,  Textual support,  French

Record number: 1, Textual support number: 1 DEF

La plus ancienne des dimensions fractales possibles, assignée en 1918 par Felix Hausdorff aux courbes de type flocon de neige et développée en 1935 par Besicovitch.  2, record 1, French, - dimension%20de%20Hausdorff%2DBesicovitch

Record number: 1, Textual support number: 1 OBS

Le concept mathématique «dimension de Hausdorff» constitue une généralisation de la notion de dimension euclidienne.  2, record 1, French, - dimension%20de%20Hausdorff%2DBesicovitch

Record 1,  Textual support,  Spanish

Record 2,  Textual support,  English

Record number: 2, Textual support number: 1 DEF

A non-zero but finite s-dimensional Hausdorff measure.  2, record 2, English, - Besicovitch%20measure

Record number: 2, Textual support number: 1 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.  3, record 2, English, - Besicovitch%20measure

Record 2,  Textual support,  French

Record number: 2, Textual support number: 1 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.  1, record 2, French, - mesure%20de%20Besicovitch

Record 2,  Textual support,  Spanish

Record 3,  Textual support,  English

Record number: 3, Textual support number: 1 CONT

More generally, whenever S is of zero Lebesgue measure one can prove that Df is finite and at most equal to the Hausdorff Besicovitch dimension D of S.  2, record 3, English, - zero%20Lebesgue%20measure

Record 3,  Textual support,  French

Record 3,  Textual support,  Spanish