English- translations for hausdorff dimension

Definition of hausdorff dimension

• 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

Examples

• 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.

Related words

• exhaust
• Hausa
• exhausting
• exhaustive
• exhaustion
• exhausted
• exhaustively
• haustorium
• Schaffhausen
• chausse