Mirko Sardella, Dipartimento di Matematica, Politecnico, corso Duca degli Abruzzi 24, 10129 Torino, Italy, e-mail: sardella@calvino.polito.it; Guido Ziliotti, Universita di Pisa, Dipartimento di Matematica, via F. Buonarroti 56100 Pisa, Italy, e-mail: ziliotti@dm.unipi.it
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 (MSC 2000): 28A20, 28E15
Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.