Abstract: In this note, we prove that the countable compactness of \set \^^Mtogether with the Countable Axiom of Choice yields the existence of a nonmeasurable subset of $\re $. This is done by providing a family of nonmeasurable subsets of $\re $ 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.
Keywords: Lebesgue measure, nonmeasurable set, axiom of choice
Classification (MSC2000): 28A20, 28E15
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