薛红,王拉省.实值非负函数关于集值序增函数的集值Riemann-Stieltjes积分[J].数学研究及应用,2007,27(1):135~144
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
投稿时间:2004-10-21  修订日期:2005-07-12
DOI:10.3770/j.issn:1000-341X.2007.01.019
中文关键词:  集值序增过程  集值Riemann-Stieltjes积分  集值随机积分.
英文关键词:set-valued order increasing process  set-valued Riemann-Stieltjes integral  set-valued Riemann-Stieltjes stochastic integral.
基金项目:陕西省教育厅自然科学专项基金(03JK063)
作者单位
薛红 西安工程大学理学院, 陕西 西安 710048 
王拉省 西安工程大学理学院, 陕西 西安 710048 
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中文摘要:
      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.
英文摘要:
      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.
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