Games characterizing limsup functions and Baire class 1 functions

Abstract

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 : T → R such that f (x) = lim sup t→∞ u(x 0 , . . . , x t ) for each x ∈ X. We study a game characterization of limsup functions, as well as a novel game characterization of functions of Baire class 1.

Games characterizing certain families of functions

“…This improved the results by Duparc [7] and Carroy [6] that have been mentioned above. Another idea characterizing Baire 1, real-valued functions, has been presented in [8].…”