The Kestelman-Borwein-Ditor Theorem asserts that a non-negligible subset of $\mathbb{R}$ which is Baire (= has the Baire property, BP) or measurable is shift-compact: it contains some subsequence of any null sequence to within translation by an element of the set. Here effective proofs are recognized to yield (i) analogous category and Haar-measure metrizable generalizations for Baire groups and locally compact groups respectively, and (ii) permit under $V=L$ construction of co-analytic shift-compact subsets of $\mathbb{R}$ with singular properties, e.g. being concentrated on $\mathbb{Q}$, the rationals.

中文翻译：

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除Erdős-Kunen-Mauldin之外：Shift-紧凑性和奇异集

Kestelman-Borwein-Ditor定理断言，的不可忽略子集 $\mathbb{[R}$是Baire（=具有Baire属性，BP）或可度量的是移位紧凑的：它包含该集合的元素在翻译范围内的任何空序列的子序列。在这里，有效的证据被认为可以分别产生（i）Baire组和局部紧致组的类似类别和Haar度量可度量的概括，并且（ii）允许根据$V=\mathrm{大号}$ 的协分析移位压缩子集的构建 $\mathbb{[R}$ 具有独特的性质，例如集中于 $\mathbb{问}$，理性。