The Baire order of the functions continuous almost everywhere
R. D. Mauldin · Proceedings of the American Mathematical Society · 1973
Let Φ \Phi be the family of all real-valued functions defined on the unit interval I I which are continuous except for a set of Lebesgue measure zero. Let Φ 0 {\Phi _0} be Φ \Phi and for each ordinal α \alpha , let Φ α {\Phi _\alpha } be the family of all pointwise limits of sequences taken from ⋃ γ > α Φ γ \bigcup olimits _{\gamma > \alpha } {{\Phi _\gamma }} Then Φ ω 1 {\Phi _{{\omega _1}}} is the Baire family generated by Φ \Phi . It is proven here that if 0 > α > ω 1 0 > \alpha > {\omega _1} , then