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Integrable Functions Versus a Generalization of Lebesgue Points in Locally Compact Groups

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Basu S., Department of Mathematics Govt College of Engg and Textile Technology 12 W. C. R., sanjibbasu08@gmail.com

Acta Universitatis Lodziensis. Folia Mathematica

2013

tom vol. 18

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.

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1 Acta Universitatis Lodziensis. Folia Mathematica

1 Basu S.

1 Department of Mathematics Govt College of Engg and Textile Technology 12 W. C. R.

1 sanjibbasu08@gmail.com

1 2013

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Integrable Functions Versus a Generalization of Lebesgue Points in Locally Compact Groups