闭集的有效容量与随机性
Effective Capacity and Randomness of Closed Sets
摘要：
本文研究了{0，1}* 的非空闭子集空间的测度与容度之间的关系。对于任何可计算测度，可计算容量T可以通过令T（Q）是与Q有非空交集的闭集族的测度来定义。我们证明了一个有效的版本Choquet的能力定理表明，每一个可计算的能力，可以得到一个可计算的措施，以这种方式。我们建立了随机闭集的容量等于零或大于0的条件。我们构造了一个有效的封闭集，具有正容量和勒贝格测度为零。
英文摘要：
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.
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。
