Bernstein set
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Names in other languages
- РусскийМножество Бернштейна
- PolskiZbiór Bernsteina
- EnglishBernstein set
Article bodies are English and are not machine-translated. A name in another language is not a translation of the article.
In mathematics, a Bernstein set is a subset of the real line that meets every uncountable closed subset of the real line but that contains none of them. A Bernstein set partitions the real line into two pieces in a peculiar way: every measurable set of positive measure meets both the Bernstein set and its complement, as does every set with the property of Baire that is not a meagre set.
In mathematics, a Bernstein set is a subset of the real line that meets every uncountable closed subset of the real line but that contains none of them. A Bernstein set partitions the real line into two pieces in a peculiar way: every measurable set of positive measure meets both the Bernstein set and its complement, as does every set with the property of Baire that is not a meagre set. ==References==
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