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2010•jOURNAL OF southwest University for NationalitiesRequires access

Properties and existence theorems of set-valued function Riemann-Stieltjes integral

Aihong Ren

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Abstract

This paper uses definition of set-valued Riemann-Stieltjes integral of set-valued function with respect to real non-decreasing function,studies some properties of set-valued Riemann-Stieltjes integral,and then gives existence theorems of set-valued Riemann-Stieltjes integral of set-valued function on real non-decreasing function.These results play important roles in further studying set-valued order increasing function.

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What this paper is about

This paper uses definition of set-valued Riemann-Stieltjes integral of set-valued function with respect to real non-decreasing function,studies some properties of set-valued Riemann-Stieltjes integral,and then gives existence theorems of set-valued Riemann-Stieltjes integral of set-valued function on real non-decreasing function.These results play important roles in further studying set-valued order increasing function.

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Available abstract

This paper uses definition of set-valued Riemann-Stieltjes integral of set-valued function with respect to real non-decreasing function,studies some properties of set-valued Riemann-Stieltjes integral,and then gives existence theorems of set-valued Riemann-Stieltjes integral of set-valued function on real non-decreasing function.These results play important roles in further studying set-valued order increasing function.

Key concepts: Riemann–Stieltjes integral, Mathematics, Riemann integral, Function (biology), Set (abstract data type), Set function, Daniell integral, Pure mathematics

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