卑微的观念、尺度和支配
Lowness notions, measure and domination
摘要：
我们表明，积极的措施支配意味着统一的几乎处处支配，这个证明转化为一个证明在子系统WWKL $_0$（但不是在RCA $_0$）的等价性的各种勒贝格测度正则性陈述介绍了Dobrinen和辛普森。这项工作还使我们能够证明，弱$2$ -随机性的低与马丁-勒夫随机性的低相同（Nies独立获得的结果）。使用相同的技术，我们证明了$\leq_{LR}$蕴涵$\leq_{LK}$，推广了马丁-洛夫随机性低意味着$K$低的事实。
英文摘要：
We show that positive measure domination implies uniform almost everywhere domination and that this proof translates into a proof in the subsystem WWKL$_0$ (but not in RCA$_0$) of the equivalence of various Lebesgue measure regularity statements introduced by Dobrinen and Simpson. This work also allows us to prove that low for weak $2$-randomness is the same as low for Martin-Löf randomness (a result independently obtained by Nies). Using the same technique, we show that $\leq_{LR}$ implies $\leq_{LK}$, generalizing the fact that low for Martin-Löf randomness implies low for $K$.
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