\begin{definition}[Definition:Baire Function]
Let $X \subseteq \R$. 
For each $n$, let $f_n : X \to \R$ be a continuous function.
Suppose that the sequence $\sequence {f_n}$ converges pointwise to a function $f : X \to \R$. 
We call $f$ a '''Baire function'''.
\end{definition}