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A Bernstein set partitions the real line into two pieces in a peculiar way: every set of positive outer measure meets both the Bernstein set and its complement, as does every set with the property of Baire that is not a meagre set.
- Oxtoby, John C. (1980). Measure and Category (2nd ed.). p. 24.
- John C. Oxtoby, Measure and Category, 2nd edition (1980)