Temat: σ-algebra - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Relatively perfect σ-algebras for flows
Autorzy:: Blanchard, F.
Kamiński, B.
Powiązania:: https://bibliotekanauki.pl/articles/1289369.pdf
Data publikacji:: 1995
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: entropy
flow
principal factor
relatively excellent σ-algebra
relatively perfect σ-algebra
Opis:: We show that for every ergodic flow, given any factor σ-algebra ℱ, there exists a σ-algebra which is relatively perfect with respect to ℱ. Using this result and Ornstein's isomorphism theorem for flows, we give a functorial definition of the entropy of flows.
Źródło:: Studia Mathematica; 1995, 114, 1; 71-85
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

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

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