| 词条 | Bernstein set |
| 释义 |
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.[1] 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.[2] References1. ^{{Cite book|last=Oxtoby|first=John C.|title=Measure and Category|edition=2nd|year=1980|page=24}} 2. ^{{citation|title=Point Set Theory|volume=131|series=Chapman & Hall/CRC Pure and Applied Mathematics|first=John C., II|last=Morgan|publisher=CRC Press|year=1989|isbn=9780824781781|page=163|url=https://books.google.com/books?id=WwmvxtDlz9UC&pg=PA163}}. 1 : Mathematical structures |
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