文章基本信息

标题：Effective Capacity and Randomness of Closed Sets
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作者：Douglas Cenzer ; Paul Brodhead
期刊名称：Electronic Proceedings in Theoretical Computer Science
电子版ISSN：2075-2180
出版年度：2010
卷号：24
页码：67-76
DOI：10.4204/EPTCS.24.11
出版社：Open Publishing Association
摘要：We investigate the connection between measure and capacity for the space of nonempty closed subsets of 0,1*. For any computable measure, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed sets which have nonempty intersection with Q. We prove an effective version of Choquet's capacity theorem by showing that every computable capacity may be obtained from a computable measure in this way. We establish conditions that characterize when the capacity of a random closed set equals zero or is >0. We construct for certain measures an effectively closed set with positive capacity and with Lebesgue measure zero.