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B

Baire class The Baire classes Bα are an increasing sequence of families of functions defined inductively for α < ω1. B0 is the set of continuous functions. For α > 0, f is in Baire class α if there is a sequence of functions {fn} converging pointwise to f , with fn ∈ Bβn and βn < α for each n. Thus, f is in Baire class 1 (or is Baire-1) if it is the pointwise limit of a sequence of continuous functions. In some cases, it is useful to define the classes so that if f ∈ Bα , then f /∈ Bβ for any β < α. See also Baire function.