77
个编辑
更改
→Examples
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)。
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实例==
[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.<ref name=ClaytonSCTPLS96/>]]
[[Image:Sierpinski deep.svg|thumb|250px|Dimension of a further [[fractal]] example. The [[Sierpinski triangle]], an object with Hausdorff dimension of log(3)/log(2)≈1.58.<ref name=ClaytonSCTPLS96/>]]
Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]
Dimension of a further [[fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.]]
进一步的分形维数的例子是谢尔宾斯基三角形，它是一个豪斯多夫维数为3 / log (2)≈1.58的物体]
* [[Countable set]]s have Hausdorff dimension 0.<ref name="schleicher">{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}</ref>
* [[Countable set]]s have Hausdorff dimension 0.<ref name="schleicher">{{cite journal |last1=Schleicher |first1=Dierk |title=Hausdorff Dimension, Its Properties, and Its Surprises |journal=The American Mathematical Monthly |date=June 2007 |volume=114 |issue=6 |pages=509–528 |doi=10.1080/00029890.2007.11920440 |language=en |issn=0002-9890|arxiv=math/0505099 }}</ref>
* [[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].<ref name="mandelbrot" />
* [[Lewis Fry Richardson]] has performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of [[South Africa]] to 1.25 for the west coast of [[Great Britain]].<ref name="mandelbrot" />
==Properties of Hausdorff dimension==
==Properties of Hausdorff dimension==