What’s the price of a nonmeasurable set?

Title:

What’s the price of a nonmeasurable set?

Creator:

Sardella, Mirko and Ziliotti, Guido

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a918d36f-145b-4d26-8c59-04ae3d6ad0cd
uuid:a918d36f-145b-4d26-8c59-04ae3d6ad0cd
doi:10.21136/MB.2002.133985

Subject:

Lebesgue measure, nonmeasurable set, and axiom of choice

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

41-48

Source:

Mathematica bohemica | 2002 Volume:127 | Number:1

Harvested from:

CDK

Metadata only:

false