算法随机闭集与有效维数的交
The intersection of algorithmically random closed sets and effective dimension
摘要：
本文研究了算法随机闭集的交的几个方面。首先，我们回答了Cenzer和Weber的一个问题，表明保持随机性的相对随机闭集相交运算（相对于闭集码空间上的伯努利测度诱导的某些底层测度）可以被逆：可以获得适当类型的随机闭集作为两个相对随机闭集的交集。然后，我们将Cenzer/Weber分析扩展到多个随机闭集的交集，确定相对于相对随机闭集的交集可以是非空的Bernoulli测度。最后，我们应用我们的分析提供了一个表征的有效豪斯多夫维数的序列的随机闭集，包含它们的可相交性的程度。
英文摘要：
In this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of intersecting relatively random closed sets (with respect to certain underlying measures induced by Bernoulli measures on the space of codes of closed sets), which preserves randomness, can be inverted: a random closed set of the appropriate type can be obtained as the intersection of two relatively random closed sets. We then extend the Cenzer/Weber analysis to the intersection of multiple random closed sets, identifying the Bernoulli measures with respect to which the intersection of relatively random closed sets can be non-empty. We lastly apply our analysis to provide a characterization of the effective Hausdorff dimension of sequences in terms of the degree of intersectability of random closed sets that contain them.
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