New smoothness conditions on Riesz spaces with applications to nonadditive measures and Choquet integrals

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It is well known that the ε-δargument plays an important role in the proof of many theorems in nonadditive measure theory and in Choquet integration theory. That is why new concepts and techniques for proving are required to develop these studies for Riesz space-valued nonadditive measures. In this research, Riesz space-valued nonadditive measure theory and their Choquet integration thoery are developed with the help of new smoothness conditions on Riesz spaces such as the asymptotic Egoroff property, the multiple Egoroff property, and the monotone function continuity property.