实值非负函数关于集值序增函数的集值Riemann-Stieltjes积分

Set-Valued Riemann-Stieltjes Integral of Real Non-Negative Function with Respect to Set-Valued Order Increasing Function

本文首先建立了实值非负函数关于集值序增函数的集值Riemann-Stieltjes积分,并讨论了集值Riemann-Stieltjes积分的性质,给出了集值Riemann-Stieltjes可积的充要条件,最后引入了集值Riemann-Stieltjes随机积分．

In this paper, we establish the set-valued Riemann-Stieltjes integral of a real valued non- negative function with respect to set-valued order increasing function. Then, we discuss the properties of the set-valued Riemann-Stieltjes integral. Some sufficent and necessary conditions for Riemann-Stieltjes integrability are obtained. Finally, we introduce the set-valued Riemann-Stieltjes stochastic integral.