Mandelbrot渗流的孔隙度
Porosities of Mandelbrot Percolation
摘要：
我们研究了Mandelbrot渗流过程中的孔隙率。我们表明，几乎肯定在几乎所有的点上的自然措施，平均孔隙率的集合和自然措施存在，并等于彼此的所有参数值以外的可数例外集。作为一个推论，我们得到，几乎肯定在几乎所有的点上，集合的下孔隙度和自然测度都等于零，而上孔隙度获得它们的最大值。
英文摘要：
We study porosities in the Mandelbrot percolation process. We show that, almost surely at almost all points with respect to the natural measure, the mean porosities of the set and the natural measure exist and are equal to each other for all parameter values outside of a countable exceptional set. As a corollary, we obtain that, almost surely at almost all points, the lower porosities of the set and the natural measure are equal to zero, whereas the upper porosities obtain their maximum values.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
