- Tytuł:
- Ramsey, Lebesgue, and Marczewski sets and the Baire property
- Autorzy:
- Reardon, Patrick
- Powiązania:
- https://bibliotekanauki.pl/articles/1205503.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Ramsey set
Marczewski set
perfect set
measurable set
Baire property
density topology
Ellentuck topology
σ-algebra - Opis:
-
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. - Źródło:
-
Fundamenta Mathematicae; 1996, 149, 3; 191-203
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł