Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions of intersections and Cartesian products of fractals in Euclidean spaces. This approach shows that two prominent, fundamental results about the dimension of Borel or analytic sets also hold for arbitrary sets.

翻译：单点的算法信息密度可以量化,并可以用科尔莫戈罗夫复杂程度来界定。这项工作利用这些维度将古典霍斯多夫和欧克莱底空间的十字路口和笛卡尔产品包装维度捆绑起来。这种方法表明,波雷尔或分析机组的维度的两个突出的基本结果也具有任意性。