- 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