Geodesic
Integrable Functions Versus a Generalization of Lebesgue Points in Locally Compact Groups
Acta Universitatis Lodziensis. Folia Mathematica, Tome 18 (2013).

Voir la notice de l'article provenant de la source University of Lodz Repository

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 R?, where by a Lebesgue class (corresponding to some x in 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.
Mots-clés : 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 
@article{AULFM_2013_18_a2,
     author = {Basu, Sanji},
     title = {Integrable {Functions} {Versus} a {Generalization} of {Lebesgue} {Points} in {Locally} {Compact} {Groups}},
     journal = {Acta Universitatis Lodziensis. Folia Mathematica},
     publisher = {mathdoc},
     volume = {18},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AULFM_2013_18_a2/}
}
TY  - JOUR
AU  - Basu, Sanji
TI  - Integrable Functions Versus a Generalization of Lebesgue Points in Locally Compact Groups
JO  - Acta Universitatis Lodziensis. Folia Mathematica
PY  - 2013
VL  - 18
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AULFM_2013_18_a2/
LA  - en
ID  - AULFM_2013_18_a2
ER  - 
%0 Journal Article
%A Basu, Sanji
%T Integrable Functions Versus a Generalization of Lebesgue Points in Locally Compact Groups
%J Acta Universitatis Lodziensis. Folia Mathematica
%D 2013
%V 18
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AULFM_2013_18_a2/
%G en
%F AULFM_2013_18_a2
Basu, Sanji. Integrable Functions Versus a Generalization of Lebesgue Points in Locally Compact Groups. Acta Universitatis Lodziensis. Folia Mathematica, Tome 18 (2013). http://geodesic.mathdoc.fr/item/AULFM_2013_18_a2/