Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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})$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 26A21

Retrieve articles in all journals with MSC: 26A21


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0637714-8
PII: S 0002-9947(1982)0637714-8
Keywords: Approximately continuous, almost everywhere continuous, Baire function
Article copyright: © Copyright 1982 American Mathematical Society