UNIFORM-CONVERGENCE OF PROBABILITY-MEASURES ON CLASSES OF FUNCTIONS

被引：1
|
作者：
BICKEL, PJ
MILLAR, PW
机构：
[1] UNIV CALIF BERKELEY,DEPT STAT,BERKELEY,CA 94720
[2] UNIV CALIF BERKELEY,DEPT STAT,BERKELEY,CA 94720
来源：
STATISTICA SINICA | 1992年 / 2卷 / 01期
关键词：
WEAK CONVERGENCE OF PROBABILITIES; UNIFORM CONVERGENCE OF PROBABILITIES; POLYA CLASS; POLYAS THEOREM; GLIVENKO-CANTELLI THEOREM; DUAL LIPSCHITZ NORM; BRACKETING; VAPNIK-CERVONENKIS CLASS; CONVEX SETS; UNIFORMITY CLASS; DELTA-TIGHT;
D O I：
暂无
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Let P(n), P be probabilities, and F, F- be collections of real functions. Simple conditions are derived under which the simple convergence of integral f(x)P(n)(dx) to integral f(x)P(dx) for every f in F- implies uniform convergence over F: sup(f is-an-element-of F) \ integral f(x)P(n) (dx) - integral f(x)P(dx)\ converges to 0. Several examples are discussed, some historical and some new.
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页码：1 / 15
页数：15
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