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第126行： − 换句话说，math c h ^ d (s) / math 是数字集合 math delta geq 0 / math 的下确界，使得在 i / math 中存在一些球集合 math { b (xi，ri) : i 包含 s，对于每个 i ∈ i，r 子 i / sub 0满足 i 中的数学和 i ^ d delta / math。(在这里，我们使用 inf ∞ .)的标准约定+
→Hausdorff content豪斯多夫集
Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by
Let X be a metric space. If S ⊂ X and d ∈ [0, ∞), the d-dimensional unlimited Hausdorff content of S is defined by
设 x 是度量空间。若 s something x 和 d ∈[0，∞) ，则 s 的 d 维无限 豪斯多夫集定义为
设 ''X''是度量空间。若''S'' ⊂ ''X'' 和 ''d'' ∈ [0, ∞) ，则 ''S'' 的''d''维无限 豪斯多夫集定义为
:<math>C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}.</math>
:<math>C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}.</math>
<math>C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}.</math>
<math>C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}.</math>
数学 c h ^ d (s) : inf Bigl sum i r i ^ d: text { there is a cover of } s text { by balls with radii } r i 0 Bigr } . / math
数学<math>C_H^d(S):=\inf\Bigl\{\sum_i r_i^d:\text{ there is a cover of } S\text{ by balls with radii }r_i>0\Bigr\}.</math>
In other words, <math>C_H^d(S)</math> is the [[infimum]] of the set of numbers <math>\delta \geq 0</math> such that there is some (indexed) collection of [[ball (mathematics)|ball]]s <math>\{B(x_i,r_i):i\in I\}</math> covering ''S'' with ''r<sub>i</sub>'' > 0 for each ''i'' ∈ ''I'' that satisfies <math>\sum_{i\in I} r_i^d<\delta </math>. (Here, we use the standard convention that [[infimum|inf Ø = ∞]].)
In other words, <math>C_H^d(S)</math> is the [[infimum]] of the set of numbers <math>\delta \geq 0</math> such that there is some (indexed) collection of [[ball (mathematics)|ball]]s <math>\{B(x_i,r_i):i\in I\}</math> covering ''S'' with ''r<sub>i</sub>'' > 0 for each ''i'' ∈ ''I'' that satisfies <math>\sum_{i\in I} r_i^d<\delta </math>. (Here, we use the standard convention that [[infimum|inf Ø = ∞]].)
In other words, <math>C_H^d(S)</math> is the infimum of the set of numbers <math>\delta \geq 0</math> such that there is some (indexed) collection of balls <math>\{B(x_i,r_i):i\in I\}</math> covering S with r<sub>i</sub> > 0 for each i ∈ I that satisfies <math>\sum_{i\in I} r_i^d<\delta </math>. (Here, we use the standard convention that inf Ø = ∞.)
In other words, <math>C_H^d(S)</math> is the infimum of the set of numbers <math>\delta \geq 0</math> such that there is some (indexed) collection of balls <math>\{B(x_i,r_i):i\in I\}</math> covering S with r<sub>i</sub> > 0 for each i ∈ I that satisfies <math>\sum_{i\in I} r_i^d<\delta </math>. (Here, we use the standard convention that inf Ø = ∞.)
换句话说， <math>C_H^d(S)</math> 是数字集合 <math>\delta \geq 0</math> 的下确界，使得在 i / math 中存在一些球集合 <math>\{B(x_i,r_i):i\in I\}</math> i 包含 s，对于每个 ''r<sub>i</sub>'' > 0 满足 i 中的和<math>\sum_{i\in I} r_i^d<\delta </math> (在这里，我们使用inf Ø = ∞ )的标准约定。
===Hausdorff measurement豪斯多夫分形测量===
===Hausdorff measurement豪斯多夫分形测量===