概率非随机对象的普适量度
The universal measure of probabilistically nonrandom objects
AI总结：
本文以普适量度衡量概率非随机对象的数量，证明其测度极小，并揭示其与所需概率随机程度的依赖关系。
AI中文摘要：
一个有限对象被称为概率随机的，如果它是某个Kolmogorov复杂度相对较小的有限集合中的算法随机元素。本文研究了概率非随机对象（即那些不是概率随机的对象）的数量，以普适量度来衡量，且不假设对象具有任何结构。主要结果表明，概率非随机对象的普适量度极小，并确立了其普适量度对所需概率随机程度的依赖关系。
英文摘要：
A finite object is called probabilistically random if it is an algorithmically random element of a finite set whose Kolmogorov complexity is relatively small. This note studies the amount of probabilistically nonrandom objects (those that are not probabilistically random) as gauged by the universal measure and without assuming any structure on the objects. The main results imply that the universal measure of probabilistically nonrandom objects is vanishingly small and establish the dependence of their universal measure on the required degree of probabilistic randomness.
