Properties of the Riemann-Lebesgue integrability in the non-additive case

Abstract

We study Riemann-Lebesgue integrability of a vector function relative to an arbitrary non-negative set function. We obtain some classical integral properties. Results regarding the continuity properties of the integral and relationships among Riemann-Lebesgue, Birkhoff simple and Gould integrabilities are also established.

arXiv comment16 pages

References in corpus (5)

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• An extension of the Birkhoff integrability for multifunctions
• Relations among Gauge and Pettis integrals for $cwk(X)$-valued multifunctions
• Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures
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