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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Classes of Baire functions

Authors: Gregory V. Cox and Paul D. Humke
Journal: Trans. Amer. Math. Soc. 269 (1982), 627-635
MSC: Primary 26A21
MathSciNet review: 637714
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Abstract: Let $ \mathcal{A}$ and $ \mathcal{P}$ denote the sets of approximately continuous and almost everywhere continuous functions, and $ {B_1}(F)$ denote Baire's first class generated by $ F$. The classes $ {B_1}(\mathcal{A})$, $ {B_1}(\mathcal{P})$, $ {B_1}(\mathcal{A} \cap \mathcal{P})$, and Grande's class $ \mathcal{A}{\mathcal{P}_1}$ are investigated in some detail. Although Grande's question of whether $ {B_1}(\mathcal{A} \cap \mathcal{P}) = {B_1}(\mathcal{A}) \cap {B_1}(\mathcal{A}) \cap \mathcal{A}{\mathcal{P}_1}$ is not settled, we do show, among other results, that $ \mathcal{A}{\mathcal{P}_1} \subset {B_1}(\mathcal{P})$.

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PII: S 0002-9947(1982)0637714-8
Keywords: Approximately continuous, almost everywhere continuous, Baire function
Article copyright: © Copyright 1982 American Mathematical Society