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    Wyświetlanie 1-6 z 6
    Tytuł:
    Strong meager properties for filters
    Autorzy:
    Laflamme, Claude
    Powiązania:
    https://bibliotekanauki.pl/articles/1208397.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    filter
    meager
    Baire property
    Opis:
    We analyze several "strong meager" properties for filters on the natural numbers between the classical Baire property and a filter being $F_σ$. Two such properties have been studied by Talagrand and a few more combinatorial ones are investigated. In particular, we define the notion of a P⁺-filter, a generalization of the traditional concept of P-filter, and prove the existence of a non-meager P⁺-filter. Our motivation lies in understanding the structure of filters generated by complements of members of a maximal almost disjoint family.
    Źródło:
    Fundamenta Mathematicae; 1994-1995, 146, 3; 283-293
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Marczewski-Burstin-like characterizations of σ-algebras, ideals, and measurable functions
    Autorzy:
    Brown, Jack
    Elalaoui-Talibi, Hussain
    Powiązania:
    https://bibliotekanauki.pl/articles/965993.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Baire property
    Marczewski measurable
    Lebesgue measurable
    Opis:
    ℒ denotes the Lebesgue measurable subsets of ℝ and $ℒ_0$ denotes the sets of Lebesgue measure 0. In 1914 Burstin showed that a set M ⊆ ℝ belongs to ℒ if and only if every perfect P ∈ ℒ\$ℒ_0$ has a perfect subset Q ∈ ℒ\$ℒ_0$ which is a subset of or misses M (a similar statement omitting "is a subset of or" characterizes $ℒ_0$). In 1935, Marczewski used similar language to define the σ-algebra (s) which we now call the "Marczewski measurable sets" and the σ-ideal $(s^0)$ which we call the "Marczewski null sets". M ∈ (s) if every perfect set P has a perfect subset Q which is a subset of or misses M. M ∈ $(s^0)$ if every perfect set P has a perfect subset Q which misses M. In this paper, it is shown that there is a collection G of $G_δ$ sets which can be used to give similar "Marczewski-Burstin-like" characterizations of the collections $B_w$ (sets with the Baire property in the wide sense) and FC (first category sets). It is shown that no collection of $F_σ$ sets can be used for this purpose. It is then shown that no collection of Borel sets can be used in a similar way to provide Marczewski-Burstin-like characterizations of $B_r$ (sets with the Baire property in the restricted sense) and AFC (always first category sets). The same is true for U (universally measurable sets) and $U_0$ (universal null sets). Marczewski-Burstin-like characterizations of the classes of measurable functions are also discussed.
    Źródło:
    Colloquium Mathematicum; 1999, 82, 2; 277-286
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On some subclasses of the family of Darboux Baire 1 functions
    Autorzy:
    Ivanova, G.
    Wagner-Bojakowska, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/255127.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Darboux property
    Baire property
    I-approximate continuity
    quasi-continuity
    strong Świątkowski property
    Opis:
    We introduce a subclass of the family of Darboux Baire 1 functions f : R → R modifying the Darboux property analogously as it was done by Z. Grande in [On a subclass of the family of Darboux functions, Colloq. Math. 17 (2009), 95–104], and replacing approximate continuity with I-approximate continuity, i.e. continuity with respect to the I-density topology. We prove that the family of all Darboux quasi-continuous functions from the first Baire class is a strongly porous set in the space DB1 of Darboux Baire 1 functions, equipped with the supremum metric.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 777-788
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Tytuł:
    Integrable Functions Versus a Generalization of Lebesgue Points in Locally Compact Groups
    Autorzy:
    Basu, Sanji
    Powiązania:
    https://bibliotekanauki.pl/articles/972269.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    Baire-property
    Carathe odory function
    demi-spheres
    Haar measure
    Kuratowski-Ulam theorem
    Lebesgue density
    Lebesgue set
    Lebesgue class
    locally compact groups
    AMS Subject Classification. Primary 28A
    Opis:
    Here in this paper we intend to deal with two questions: How large is a “Lebesgue Class” in the topology of Lebesgue integrable functions, and also what can be said regarding the topological size of a “Lebesgue set” in \( \mathbb{R} \)?, where by a Lebesgue class (corresponding to some \( x \in \mathbb{R} \)) is meant the collection of all Lebesgue integrable functions for each of which the point \( x \) acts as a common Lebesgue point, and, by a Lebesgue set (corresponding to some Lebesgue integrable function \( f \)) we mean the collection of all ebesgue points of \( f \). However, we answer these two questions in a more general setting where in place of Lebesgue integration we use abstract integration in locally compact Hausdorff topological groups.
    Źródło:
    Acta Universitatis Lodziensis. Folia Mathematica; 2013, 18; 21-32
    2450-7652
    Pojawia się w:
    Acta Universitatis Lodziensis. Folia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Baire measurability of \((M,N)\)-Wright convex functions
    Autorzy:
    Lewicki, Michał
    Powiązania:
    https://bibliotekanauki.pl/articles/746698.pdf
    Data publikacji:
    2008
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Wright convexity
    functional inequalities
    regularity property
    Baire measurable functions
    continuous functions
    Opis:
    Let \(I \subset \mathbb{R}\) be an open interval and \(M, N \colon I^2 \to I\) be means on \(I\). Let \(\varphi\colon I \to \mathbb{R}\) be a solution of the functional equation \[ \varphi(M (x, y)) + \varphi(N (x, y)) = \varphi(x) + \varphi(y),\quad x, y \in I \] We give sufficient conditions on \(M, N\) and the function \(\varphi\) such that for every Baire measurable solution \(f \colon I \to \mathbb{R}\) of the functional inequality \[ f (M (x, y)) + f (N (x, y)) \leq f (x) + f (y),\quad x, y \in I, \] the function \(f \circ \varphi^{-1} \colon \varphi(I) \to \mathbb{R}\) is convex.
    Źródło:
    Commentationes Mathematicae; 2008, 48, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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