Geodesic
Ramsey, Lebesgue, and Marczewski sets and the Baire property
Fundamenta Mathematicae, Tome 149 (1996) no. 3, pp. 191-203

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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 $B_r$-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.
DOI : 10.4064/fm-149-3-191-203
Keywords: Ramsey set, Marczewski set, perfect set, measurable set, Baire property, density topology, Ellentuck topology, σ-algebra

Patrick Reardon 1

1 
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Patrick  Reardon. Ramsey, Lebesgue, and Marczewski sets and the Baire property. Fundamenta Mathematicae, Tome 149 (1996) no. 3, pp. 191-203. doi: 10.4064/fm-149-3-191-203

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