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第305行： − 这种不平等可以是绝对的。有可能找到两个维数为0的集合，其乘积的维数为1。相反，我们知道当''X''和''Y''是 '''R'''<sup>''n''</sup>的 Borel 子集时， ''X'' × ''Y''的豪斯多夫维数从上面以 ''X''的豪斯多夫维数加上 ''Y''的填充维数为界。Mattila (1995)曾就这些情况进行了讨论。+
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The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.
[[闵可夫斯基维数]]与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，闵可夫斯基维数为1。还有一些紧集的闵可夫斯基维数绝对大于豪斯多夫维数。
[[闵可夫斯基维数]]与豪斯多夫维数相似，至少和它一样大，而且在许多情况下是相等的。然而，[0,1]中有理点集的豪斯多夫维数为0，闵可夫斯基维数为1。还有一些紧集的闵可夫斯基维数严格大于豪斯多夫维数。
=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===
=== Hausdorff dimensions and Frostman measures 豪斯多夫维度和弗洛斯曼测度===
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R<sup>n</sup>, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of R<sup>n</sup>, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).
这种不平等可以是严格的。有可能找到两个维数为0的集合，其乘积的维数为1。相反，我们知道当''X''和''Y''是 '''R'''<sup>''n''</sup>的 Borel 子集时， ''X'' × ''Y''的豪斯多夫维数从上面以 ''X''的豪斯多夫维数加上 ''Y''的上填充维数为界。Mattila (1995)曾就这些情况进行了讨论。
==Self-similar sets自相似集合==
==Self-similar sets自相似集合==