Geodesic
Integrable Functions Versus a Generalization of Lebesgue Points in Locally Compact Groups
Acta Universitatis Lodziensis. Folia Mathematica, Tome 18 (2013) Cet article a éte moissonné depuis la source University of Lodz Repository

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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 
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     author = {Basu, Sanji},
     title = {Integrable {Functions} {Versus} a {Generalization} of {Lebesgue} {Points} in {Locally} {Compact} {Groups}},
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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/