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- W1976970395 abstract "Starting at $x$ in a Polish space $X$, a player selects the distribution $sigma_0$ of the next state $x_1$ from the collection $Gamma (x)$ of those distributions available and then selects the distribution $sigma_1(x_1)$ for $x_2$ from $Gamma(x_1)$ and so on. Suppose the player wins if every $x_i$ in the stochastic process $x_1, x_2,ldots$ lies in a given Borel subset $A$ of $X$, that is, if the process stays in $A$ forever. If ${(x, gamma): gamma in Gamma (x)}$ is a Borel subset of $X times mathbb{P}(X)$, where $mathbb{P}(X)$ is the natural Polish space of probability measures on $X$, and if $0 leq p leq 1$, 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." @default.
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- W1976970395 date "1991-01-01" @default.
- W1976970395 modified "2023-09-27" @default.
- W1976970395 title "A Borel Measurable Version of Konig's Lemma for Random Paths" @default.
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- W1976970395 doi "https://doi.org/10.1214/aop/1176990554" @default.
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