Three kinds of convergence and the associated -Baire classes

We consider ideal versions of pointwise, discrete and equal convergence of sequences of functions. Defining, in a natural way, ideal pointwise (discrete, equal) Baire classes of functions, we show that these classes are equal to their classical counterparts for ideals for which there is a winning strategy in a game introduced by Laflamme (1996) [10]. In the proofs we make extensive use of a characterization (in terms of filters F which are ω-diagonalizable by F -universal sets) of a winning strategy. This article extends results of Laczkovich and Recław (2009) [9], and Debs and Saint Raymond (2009) [5].