A survey on the Riemann-Lebesgue integrability in non-additive setting
Anca Croitoru, Alina Gavrilut, Alina Iosif, Anna Rita Sambucini
TL;DR
This survey reviews various results on Riemann-Lebesgue integrability when dealing with non-additive set functions, highlighting the extension of classical integration concepts to more general measures.
Contribution
It compiles and discusses existing research on Riemann-Lebesgue integrability in the context of non-additive set functions, an area less explored in traditional measure theory.
Findings
Extends classical Riemann-Lebesgue integrability to non-additive measures
Summarizes key results and methods in the field
Identifies open problems and future research directions
Abstract
We present in this survey some results regarding Riemann_Lebesgue integrability with respect to arbitrary non-additive set functions.
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Taxonomy
TopicsAdvanced Banach Space Theory · Nonlinear Differential Equations Analysis · Approximation Theory and Sequence Spaces