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

众所周知，ε-δ参数在非加性测度理论和Choquet积分理论的许多定理的证明中起着重要的作用。这就是为什么需要新的概念和证明技术来发展这些Riesz空间值非加性度量的研究。本文利用Riesz空间上的渐近Egoroff性质、多重Egoroff性质和单调函数连续性等光滑性条件，建立了Riesz空间值非加性测度理论及其Choquet积分理论。

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.