A BOREL MEASURABLE VERSION OF KONIG LEMMA FOR RANDOM-PATHS
成果类型：
Article
署名作者：
MAITRA, A; PURVES, R; SUDDERTH, W
署名单位：
University of California System; University of California Berkeley
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176990554
发表日期：
1991
页码：
423-451
关键词：
摘要：
Starting at x in a Polish space X, a player selects the distribution sigma-0 of the next state x1 from the collection GAMMA(x) of those distributions available and then selects the distribution sigma-1(x1) for x2 from GAMMA(x1) and so on. Suppose the player wins if every x(i) in the stochastic process x1, x2,... lies in a given Borel subset A of X, that is, if the process stays in A forever. If {(x, gamma): gamma epsilon GAMMA(x)} is a Borel subset of X x P(X), where P(X) is the natural Polish space of probability measures on X, and if 0 less-than-or-equal-to p less-than-or-equal-to 1, then a player can stay in A forever with probability at least p if and only if the player can stay in A up to time t with probability at least p for every Borel stop rule t. A similar result holds when the object of the game is to visit A infinitely often.