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In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or "rough" sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.

In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or "rough" sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.

在[[数学]]中，'''<font color = '#ff8000'>豪斯多夫维数Hausdorff dimension</font>'''是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的物体的维数，其中仅仅根据它们的标度和自相似性质，就可以得出结论，特定的物体ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度也通常被称为 Hausdorff-Besicovitch 维度。

在[[数学]]中，'''<font color = '#ff8000'>豪斯多夫维数Hausdorff dimension</font>'''是一种粗糙度的度量单位，或者更确切地说，分形维数，是由数学家 Felix Hausdorff 在1918年首次提出的。例如，单点的豪斯多夫维数为零，线段为1，正方形为2，立方体为3。也就是说，对于定义了一个光滑形状或一个有少数几个角的形状---- 传统几何学和科学的形状---- 的点集来说，豪斯多夫维数是一个整数，符合通常的维度意义，也称为拓扑维度。然而，还有一些公式允许计算其他不太简单的对象的维数，其中仅仅根据它们的标度和自相似特性，就可以得出结论: 特定的对象ー包括分形ー具有非整数的 Hausdorff 维数。由于阿布拉姆·萨莫伊洛维奇·贝西科维奇的重大技术进步，允许计算高度不规则或“粗糙”集的维度，这个维度通常也被称为 Hausdorff-Besicovitch 维度。