Theory of Probability &Its Applications, Volume 65, Issue 3, Page 375-387, January 2020.
We introduce the concept of $\varepsilon$-complexity of an individual continuous finite-dimensional map. This concept is in good accord with the principle of A.N. Kolmogorov's idea of measuring complexity of objects. It is shown that the $\varepsilon$-complexity of an “almost all” Hölder map can be effectively described. This description can be used as a basis for a model-free technique for segmentation and classification of data of arbitrary nature. A new definition of the dimension of the graph of a map is also proposed.

中文翻译：

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连续有限维图的复杂度和维数

概率论及其应用，第65卷，第3期，第375-387页，2020年1月。
我们介绍了单个连续有限维图的$ \ varepsilon $-复杂性的概念。该概念与AN Kolmogorov测量对象复杂性的思想的原理非常吻合。结果表明，“几乎所有”Hölder映射的$ \ varepsilon $复杂度都可以得到有效描述。该描述可以用作无模型技术的基础，该技术用于对任意性质的数据进行分割和分类。还提出了地图图形尺寸的新定义。