Definition:Baire Function
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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