1. What’s the price of a nonmeasurable set?
- Creator:
- Sardella, Mirko and Ziliotti, Guido
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Lebesgue measure, nonmeasurable set, and axiom of choice
- Language:
- English
- Description:
- In this note, we prove that the countable compactness of {0, 1} R together with the Countable Axiom of Choice yields the existence of a nonmeasurable subset of . This is done by providing a family of nonmeasurable subsets of whose intersection with every non-negligible Lebesgue measurable set is still not Lebesgue measurable. We develop this note in three sections: the first presents the main result, the second recalls known results concerning non-Lebesgue measurability and its relations with the Axiom of Choice, the third is devoted to the proofs.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public