Ramsey, Lebesgue, and Marczewski sets and the Baire property
Reardon, Patrick
Fundamenta Mathematicae, Tome 149 (1996), p. 191-203 / Harvested from The Polish Digital Mathematics Library
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We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented.  THEOREM. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets.  THEOREM. In the Ellentuck topology on [ω]ω, (s)0 is a proper subset of the hereditary ideal associated with (s).  We construct an example in the Ellentuck topology of a set which is first category and measure 0 but which is not Br-measurable. In addition, several theorems concerning perfect sets in the Ellentuck topology are presented. In particular, it is shown that there exist countable perfect sets in the Ellentuck topology.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:212118 
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     title = {Ramsey, Lebesgue, and Marczewski sets and the Baire property},
     journal = {Fundamenta Mathematicae},
     volume = {149},
     year = {1996},
     pages = {191-203},
     zbl = {0846.28002},
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Reardon, Patrick. Ramsey, Lebesgue, and Marczewski sets and the Baire property. Fundamenta Mathematicae, Tome 149 (1996) pp. 191-203. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv149i3p191bwm/

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