函数序列关于弱收敛概率测度序列积分的单调收敛定理
Monotone Convergence Theorems for the Integration of Function Sequence with respect to Weak Convergence Probability Measure Sequence
摘要
研究了函数序列关于弱收敛概率测度序列积分的单调收敛性,在新的条件下得到了单调收敛定理.
Monotone convergence theorems for the integration of function sequence with respect to weak convergence probability measure sequence are studied. And some new equivalent conditions of weak convergence of probability measure are obtained.
出处
《重庆工学院学报（自然科学版）》
2009年第7期171-174,共4页
Journal of Chongqing Institute of Technology
关键词
概率测度
弱收敛
单调收敛定理
一致可积
probabilitymeasure
weakconvergence
monotone convergencetheorem
uniformly integrable
参考文献7
-
1Lucchetti R, Salinetti G, Wets J B. Uniform convergence of probability measures : topological criteria [ J ]. Journal of Multivariates Analysis, 1994(51 ) :252 - 264.
-
2Salinetti G. Consistency of statistical estimators: the epigraphical view [ C ]//Uryasev S, Pardalos P M. stochastic Optimization : Algorithms and Applications. Dordreeht : Kluwer Academic Publishers,2001:365 - 383.
-
3Birge J R, Wets R J B. Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse [ J ]. Mathematical Programming Study, 1986,27 (1) :54 - 102.
-
4Dupacova J, Wets R J B. Asymptotic behavior of statistical estimators and of optimal solutions of optimization problems [ J ]. The Annals of Statistics, 1988,16 (4) : 1517 - 1549.
-
5Zervos M. On the epiconvergence of stochastic optimization problem [ J ]. Mathematics of Operations Research, 1999,24 (2) : 495 - 508.
-
6Artstein Z, Wets R J B. Stability results for stochastic programs and sensor, allowing for discontinuous objective functions [ J ]. SIAM Journal on Optimization, 1994,4 (3) :537 - 550.
-
7霍永亮,刘三阳.可测函数序列关于弱收敛概率测度序列积分的极限定理[J].系统科学与数学,2008,28(6):709-717. 被引量：3
二级参考文献8
-
1霍永亮,刘三阳.函数序列关于弱收敛概率测度序列积分的极限定理[J].兰州大学学报（自然科学版）,2005,41(6):125-129. 被引量：6
-
2Robinson S M and Wets R J B. Stability in two-stage stochastic programming. SIAM Journal on Control and Optimization, 1987, 25(6): 1409-1416.
-
3Birge J R and Wets R J B. Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse. Mathematical Programming Study, 1986, 27(1): 54-102.
-
4Dupacova J and Wets R J B. Asymptotic behavior of statistical estimators and of optimal solutions of optimization problems. The Annals of Statistics, 1988, 16(2): 1517-1549.
-
5Zervos M. On the epiconvergence of stochastic optimization problems. Mathematics of Operations Research, 1999, 24(2): 495-508.
-
6Lucchetti R, Salinetti G and Wets R J B. Uniform convergence of probability measures: Topological criteria. Journal of Multivariate Analysis, 1994, 51(2): 252-264.
-
7Salinetti G. Consistency of statistical estimators: The epigraphical view. S. Uryasev and P. M. Pardalos. Stochastic Optimization: Algorithms and Applications. Dordrecht: Kluwer Academic Publishers, 2001:365-383.
-
8Artstein Z and Wets R J B. Stability results for stochastic programs and sensor, allowing for discontiuous objective functions. SIAM Journal on Optimization, 1994, 4(3): 537-550.
-
1霍永亮,刘三阳.可测函数序列关于弱收敛概率测度序列积分的极限定理[J].系统科学与数学,2008,28(6):709-717. 被引量：3
-
2陈颖.函数序列关于几乎处处弱收敛概率测度序列积分的单调收敛定理[J].佳木斯大学学报（自然科学版）,2009,27(3):438-440.
-
3林一星.测度按Kakutani距离的收斂[J].龙岩师专学报,1989,7(2):27-28.
-
4霍永亮,刘三阳.函数序列关于弱收敛概率测度序列积分的控制收敛定理[J].四川大学学报（自然科学版）,2006,43(5):948-954.
-
5邓总纲.关于乘积测度的一个性质[J].长沙电力学院学报（自然科学版）,2006,21(2):70-71.
-
6徐侃,张绍义.一类可数离散半群上概率测度序列的组合收敛性[J].数学年刊（A辑）,1997,1(3):367-374. 被引量：2
-
7姚志敏,邓迎春.胎紧概率测度序列的一种构造[J].怀化学院学报,2007,26(11):1-5.
-
8王肖义,何伟弘,黄煜.真拟弱几乎周期点和拟正则点[J].中国科学：数学,2013,43(12):1185-1192. 被引量：1
-
9霍永亮,刘三阳.函数序列关于弱收敛概率测度序列积分的极限定理[J].兰州大学学报（自然科学版）,2005,41(6):125-129. 被引量：6
-
10潘继斌,左继宏.一类局部紧拓扑半群上的测度序列的淡收敛性[J].湖北师范学院学报（自然科学版）,1998,0(3):29-32.
