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

Abstract:

      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.