Shoenfield绝对性定理在uniform distribution理论中的应用
An application of Shoenfield's absoluteness theorem to the theory of uniform distribution
摘要：
如果（B_x：N中的x）是由Baire空间N = omega^omega索引的Borel集族，所有B_x都有测度零，且族是增的，则所有B_x的并也有测度零。我们给这个定理的两个证明：一个在语言的集合论，使用Shoenfield定理的Sigma-1-2集，其他的语言的概率论，使用冯诺依曼的选择定理，我们应用定理的问题完全均匀分布的序列。
英文摘要：
If (B_x: x in N) is a Borel family of sets, indexed by the Baire space N = omega^omega, all B_x have measure zero, and the family is increasing, then the union of all B_x also has measure zero. We give two proofs of this theorem: one in the language of set theory, using Shoenfield's theorem on Sigma-1-2 sets, the other in the language of probability theory, using von Neumann's selection theorem, and we apply the theorem to a question on completely uniformly distributed sequences.
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