Convergence to convex compact sets in infinite dimensions

被引：5

作者：

Artstein, Z ^{[1
]}

Gaitsgory, V

机构：

[1] Weizmann Inst Sci, Dept Math, IL-76100 Rehovot, Israel

[2] Univ S Australia, Sch Math, Mawson Lakes, SA 5095, Australia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2003年 / 284卷 / 02期

基金：

澳大利亚研究理事会; 以色列科学基金会;

关键词：

D O I：

10.1016/S0022-247X(03)00334-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a simple test for the convergence of a sequence of subsets in an infinite-dimensional space to a compact convex one. The test reduces, roughly, the convergence problem to finite dimensions. Applications are portrayed demonstrating how convexification phenomena established in finite dimensions are easily generalized to infinite dimensions. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：471 / 480

页数：10

共 14 条

[1] [Anonymous], 1985, B INSTIT MATH ACAD S
[2] STRONG LAW OF LARGE NUMBERS FOR RANDOM COMPACT SETS
ARTSTEIN, Z
VITALE, RA
[J]. ANNALS OF PROBABILITY, 1975, 3 (05) : 879 - 882
[3] CONVEXIFICATION IN LIMIT LAWS OF RANDOM SETS IN BANACH-SPACES
ARTSTEIN, Z
HANSEN, JC
[J]. ANNALS OF PROBABILITY, 1985, 13 (01) : 307 - 309
[4] Multiscale singularly perturbed control systems: Limit occupational measures sets and averaging
Gaitsgory, V
Nguyen, MT
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2002, 41 (03) : 954 - 974
[5] Limit occupational measures set for a control system and averaging of singularly perturbed control systems
Gaitsgory, V
Leizarowitz, A
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 233 (02) : 461 - 475
[6] Averaging of singularly perturbed systems
Grammel, G
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (11) : 1851 - 1865
[7] HALE JK, 1977, THEORY FUNCTIONAL DI
[8] Subadditive ergodic theorems for random sets in infinite dimensions
Hansen, JC
Hulse, P
[J]. STATISTICS & PROBABILITY LETTERS, 2000, 50 (04) : 409 - 416
[9] HIAI F, 1984, LECT NOTES MATH, V1091, P160
[10] Klein E, 1984, Theory of correspondences

← 1 2 →