127 (2002) MATHEMATICA BOHEMICA No. 1, 41–48 WHAT’S THE PRICE OF A NONMEASURABLE SET?

Abstract. In this note, we prove that the countable compactness of {0, 1} Ê together with the Countable Axiom of Choice yields the existence of a nonmeasurable subset of Ê. This is done by providing a family of nonmeasurable subsets of Ê 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