Definition:Baire Function

Definition

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.

Also see

• Results about Baire functions can be found here.

Sources

• 2008: Brian S. Thomson, Judith B. Bruckner and Andrew M. Bruckner: Elementary Real Analysis (2nd ed.) ... (previous) ... (next): $\S 1.6.2$: An illustration of a category argument