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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 with the Axiom...

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Weak convergence of monotone functions and Weyl's criterion

Weak Convergence of Vector Measures on F-Space.

Weak integrals defined on Euclidean n-space

Weak limit of measures that is not a pointwise limit on compact sets

Weakly compactly generated Frechet spaces.

What’s the price of a nonmeasurable set?

Currently displaying 1 – 6 of 6