均匀几乎处处支配
Uniform almost everywhere domination
摘要：
我们探讨了勒贝格测度与控制函数之间的相互作用。我们表明，通过一个优先建设和强制建设，有一个功能的不完整的程度，占主导地位的几乎所有程度。这回答了一个问题的多布里宁和辛普森，谁表明，这些职能是有关的证明理论强度的规律性勒贝格测度的$G_δ$集。我们的构造基本上解决了这个原理的反向数学分类。2005年11月13日修订。进行了轻微更正。
英文摘要：
We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for $G_δ$ sets. Our constructions essentially settle the reverse mathematical classification of this principle. Revised Nov 13, 2005. Minor corrections made.
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