Extensions of discrete and equal Baire functions (Q808021)

In the paper by the author and \textit{M. Laczkovich} [Studia Sci. Math. Hungar. 10, 463-472 (1975; Zbl 0405.26006)] discrete and equal convergence of sequences of real-valued functions have been introduced. Namely, we say that f is the discrete limit of \(\{f_ n\}\), if for every \(x\in X\) there exists \(n_ 0=n_ 0(x)\) such that \(f(x)=f_ n(x)\) for \(n\geq n_ 0\). Further, f is said to be the equal limit of the sequence \(\{f_ n\}\) if there is a sequence of positive numbers \(\epsilon_ n\to 0\) such that, for every \(x\in X\) there exists \(n_ 0=n(x)\) with \(| f(x)-f_ n(x)| <\epsilon_ n\), for \(n\geq n_ 0\). Subsequently, in two follow-up articles (ibid.) corresponding Baire classes of functions have been studied. In this note, extensions of the mentioned classes of functions are investigated.