An application of Shoenfield's absoluteness theorem to the theory of uniform distribution期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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An application of Shoenfield's absoluteness theorem to the theory of uniform distribution

Authors:	Martin Goldstern

Institution:	(1) 2. Mathematisches Institut, FU Berlin, D-14195 Berlin, Federal Republic of Germany

Abstract:	IfC is a Polish probability space, $W \subseteq \omega ^\omega \times \mathbb{C}$ a Borel set whose sectionsW _x ( have measure one and are decreasing $(x \leqslant x\prime \to W_x \supseteq W_{x\prime } )$ , then we show that the set _x W _x has measure one. We give two proofs of this theorem—one in the language of set theory, the other in the language of probability theory, and we apply the theorem to a question on completely uniformly distributed sequences.Supported by DFG grant Ko 490/7-1.

Keywords:	28A05 03E15 03E40 11K36
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