van Lambalgen定理的推广与条件概率的盲随机性
Generalization of van Lambalgen's theorem and blind randomness for conditional probabilities
摘要：
推广的Lambalgen定理的研究与希波克拉底（盲）随机性的概念，而不假设条件概率的可计算性。在[Bauwence 2014]中，当条件概率不可计算时，给出了推广Lambalgen定理的反例。在本文中，它表明：（一）有限的鞅盲随机性，（二）分类的两个盲随机似然比检验，（三）充分条件的推广Lambalgen定理，（四）一个例子，满足Lambalgen定理，但条件概率是不可计算的所有随机参数。
英文摘要：
Generalization of the Lambalgen's theorem is studied with the notion of Hippocratic (blind) randomness without assuming computability of conditional probabilities. In [Bauwence 2014], a counter-example for the generalization of Lambalgen's theorem is shown when the conditional probability is not computable. In this paper, it is shown that (i) finiteness of martingale for blind randomness, (ii) classification of two blind randomness by likelihood ratio test, (iii) sufficient conditions for the generalization of the Lambalgen's theorem, and (iv) an example that satisfies the Lambalgen's theorem but the conditional probabilities are not computable for all random parameters.
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。
