When is $\mathbb {R}$ the union of an increasing family of null sets?

Juan González-Hernández; Fernando Hernández-Hernández; César E. Villarreal

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What’s the price of a nonmeasurable set?

Mirko Sardella, Guido Ziliotti (2002)

Mathematica Bohemica

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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 $ℝ$ . This is done by providing a family of nonmeasurable subsets of $ℝ$ 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...