Bernstein set
From Wikipedia, the free encyclopedia
Template:DMCA 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]
References
Page Template:Reflist/styles.css has no content.
- ^ Page Module:Citation/CS1/styles.css has no content.Oxtoby, John C. (1980). Measure and Category (2nd ed.). p. 24.
- ^ Page Module:Citation/CS1/styles.css has no content.Morgan, John C. II (1989), Point Set Theory, Chapman & Hall/CRC Pure and Applied Mathematics, vol. 131, CRC Press, p. 163, ISBN 9780824781781.
