Geodesic
Vitali sets and Hamel bases that are Marczewski measurable
Fundamenta Mathematicae, Tome 166 (2000) no. 3, pp. 269-279.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We give examples of a Vitali set and a Hamel basis which are Marczewski measurable and perfectly dense. The Vitali set example answers a question posed by Jack Brown. We also show there is a Marczewski null Hamel basis for the reals, although a Vitali set cannot be Marczewski null. The proof of the existence of a Marczewski null Hamel basis for the plane is easier than for the reals and we give it first. We show that there is no easy way to get a Marczewski null Hamel basis for the reals from one for the plane by showing that there is no one-to-one additive Borel map from the plane to the reals.
DOI : 10.4064/fm-166-3-269-279

Arnold W. Miller 1 ; Strashimir G. Popvassilev 1

1 
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Arnold W. Miller; Strashimir G. Popvassilev. Vitali sets and Hamel bases that are Marczewski measurable. Fundamenta Mathematicae, Tome 166 (2000) no. 3, pp. 269-279. doi : 10.4064/fm-166-3-269-279. https://geodesic-test.mathdoc.fr/articles/10.4064/fm-166-3-269-279/

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