Autor: Solecki, Sławomir - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Filters and sequences
Autorzy:: Solecki, Sławomir
Powiązania:: https://bibliotekanauki.pl/articles/1205111.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: filters
separation property
Fatou's lemma
Opis:: We consider two situations which relate properties of filters with properties of the limit operators with respect to these filters. In the first one, we show that the space of sequences having limits with respect to a $Π^0_3$ filter is itself $Π^0_3$ and therefore, by a result of Dobrowolski and Marciszewski, such spaces are topologically indistinguishable. This answers a question of Dobrowolski and Marciszewski. In the second one, we characterize universally measurable filters which fulfill Fatou's lemma.
Źródło:: Fundamenta Mathematicae; 2000, 163, 3; 215-228
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On Haar null sets
Autorzy:: Solecki, Sławomir
Powiązania:: https://bibliotekanauki.pl/articles/1205504.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: We prove that in Polish, abelian, non-locally-compact groups the family of Haar null sets of Christensen does not fulfil the countable chain condition, that is, there exists an uncountable family of pairwise disjoint universally measurable sets which are not Haar null. (Dougherty, answering an old question of Christensen, showed earlier that this was the case for some Polish, abelian, non-locally-compact groups.) Thus we obtain the following characterization of locally compact, abelian groups: Let G be a Polish, abelian group. Then the σ-ideal of Haar null sets satisfies the countable chain condition iff G is locally compact. We also show that in Polish, abelian, non-locally-compact groups analytic sets cannot be approximated up to Haar null sets by Borel, or even co-analytic, sets; however, each analytic Haar null set is contained in a Borel Haar null set. Actually, we prove all the above results for a class of groups which is much wider than the class of all Polish, abelian groups, namely for Polish groups admitting a metric which is both left- and right-invariant.
Źródło:: Fundamenta Mathematicae; 1996, 149, 3; 205-210
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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