GAMES CHARACTERIZING LIMSUP FUNCTIONS AND BAIRE CLASS 1 FUNCTIONS
2022
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 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.
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