可计算概率空间上的随机性-一个动力学观点
Randomness on Computable Probability Spaces - A Dynamical Point of View
摘要：
我们将随机性的概念（在Schnorr介绍的版本中）扩展到可计算的概率空间，并将其与随机性的动态概念：典型性进行比较。粗略地说，如果一个点遵循系统的统计行为（伯克霍夫逐点遍历定理），那么这个点对于某些动态是典型的。我们证明了一个点是Schnorr随机的当且仅当它是典型的每一个混合可计算动力学。为了证明这一结果，我们开发了一些工具，用于可计算概率空间理论（例如，态射），这些工具预计会有其他应用。
英文摘要：
We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a dynamical notion of randomness: typicality. Roughly, a point is typical for some dynamic, if it follows the statistical behavior of the system (Birkhoff's pointwise ergodic theorem). We prove that a point is Schnorr random if and only if it is typical for every mixing computable dynamics. To prove the result we develop some tools for the theory of computable probability spaces (for example, morphisms) that are expected to have other applications.
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。
