完备度量空间上迭代函数系统的不变集性质及测度的维数是分形几何研究的主要对象。
The property of the invariant set and measure's dimension of the IFS are main objects in the studying of fractal geometry.
将分形用于自然纹理描述，指出了单一分形维数测度用于纹理分析的局限性，并提出了尺度分维的新概念。
The limitations of single fractal dimension for texture analysis are pointed out and a new concept of scale fractal dimension is proposed.
一个三分康托集与它的平移集的交集的维数与测度均与平移的长度相关。
It is discovered that the dimension and measure of the intersection of triadic Cantor sets with their translates are related to the translate length.
一个三分康托尘与它的平移集的交集的维数与测度均与平移的长度相关。
It is discovered that the dimension and measure of the intersection of triadic Cantor dust with their translates are related to the translate length.
自相似测度的研究可以追溯到上个世纪30年代，随着研究的深入，人们逐渐发现它与调和分析、代数数论、动力系统及维数的估计都有密切的联系。
The self-similar measure has been studied since 1930's, revealing connections with harmonic analysis, the theory of algebraic numbers, dynamical systems and Hausdorff dimension estimation.
自相似测度的研究可以追溯到上个世纪30年代，随着研究的深入，人们逐渐发现它与调和分析、代数数论、动力系统及维数的估计都有密切的联系。
The self-similar measure has been studied since 1930's, revealing connections with harmonic analysis, the theory of algebraic numbers, dynamical systems and Hausdorff dimension estimation.
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