具有limsup函数和Baire 1类函数的对策
Games characterizing limsup functions and Baire class 1 functions
摘要：
考虑定义在可数分枝剪枝树$T$的无限分枝集$X$上的实值函数$f$.如果存在函数$u \colon T \to \mathbb{R}$使得对于每个$x \in X$有$f(x) = \limsup_{t \to \infty} u(x_{0},\dots,x_{t})$，则函数$f$被称为\textit{limsup function}。我们研究了一个游戏的limsup函数的表征，以及一个新的游戏的功能Baire类1的表征。
英文摘要：
We consider a real-valued function $f$ defined on the set of infinite branches $X$ of a countably branching pruned tree $T$. The function $f$ is said to be a \textit{limsup function} if there is a function $u \colon T \to \mathbb{R}$ such that $f(x) = \limsup_{t \to \infty} u(x_{0},\dots,x_{t})$ for each $x \in X$. We study a game characterization of limsup functions, as well as a novel game characterization of functions of Baire class 1.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
