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arXiv 1503.06332math.LO
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琐碎的措施并不那么琐碎

Trivial measures are not so trivial

Christopher P. Porter

摘要:

虽然关于各种非均匀可计算测度的算法随机性得到了很好的研究,但很少关注关于可计算\emph{trivial}测度的算法随机性,其中如果$μ$的支持由可数序列集合组成,则$2^ω$上的测度$μ$是平凡的。在这篇文章中,它表明,有更多的结构,平凡的可计算措施比以前怀疑。

英文摘要:

Although algorithmic randomness with respect to various non-uniform computable measures is well-studied, little attention has been paid to algorithmic randomness with respect to computable \emph{trivial} measures, where a measure $μ$ on $2^ω$ is trivial if the support of $μ$ consists of a countable collection of sequences. In this article, it is shown that there is much more structure to trivial computable measures than has been previously suspected.

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。

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