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→Hausdorff dimension
数学函数 h ^ d (s) : lim { r to 0} inf Bigl sum i r i ^ d: text {有一个{ s text by balls with radii }0 r i r Bigr }的封面。 数学
数学函数 h ^ d (s) : lim { r to 0} inf Bigl sum i r i ^ d: text {有一个{ s text by balls with radii }0 r i r Bigr }的封面。 数学
===Hausdorff dimension===
===Hausdorff dimension豪斯多夫维数===
The '''Hausdorff dimension''' of ''X'' is defined by
The '''Hausdorff dimension''' of ''X'' is defined by
Equivalently, dim<sub>H</sub>(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).
Equivalently, dim<sub>H</sub>(X) may be defined as the infimum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is zero. This is the same as the supremum of the set of d ∈ [0, ∞) such that the d-dimensional Hausdorff measure of X is infinite (except that when this latter set of numbers d is empty the Hausdorff dimension is zero).
等价地，dim 子 h / sub (x)可定义为 d ∈[0，∞)集的下确界，使得 x 的 d 维 Hausdorff 测度为零。这与 d ∈[0，∞)的集合的上确界相同，因此 x 的 d 维豪斯多夫 Hausdorff 测度是无限的(除非后一个集合 d 是空的，豪斯多夫维数为零)。
等价地，dim 子 h / sub (x)可定义为 d ∈[0，∞)集的下确界，使得 x 的 d 维 Hausdorff 测度为零。这与 d ∈[0，∞)的集合的上确界相同，因此 x 的 d 维豪斯多夫测度是无限的(除非后一个集合 d 是空的，豪斯多夫维数为零)。
==Examples==
==Examples==