A Simpler Proof for the ϵ-δ Characterization of Baire Class One Functions

We offer a new and simpler proof of a recent ϵ-δ characterization of Baire class one functions using a theorem by Henri Lebesgue. The proof is more elementary in the sense that it does not use the Baire Category Theorem. Furthermore, the proof requires only that the domain and range be separable met...

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Bibliographic Details
Main Authors: Cabral, Emmanuel A, Fenecios, Jonald P
Format: text
Published: Archīum Ateneo 2015
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Online Access:https://archium.ateneo.edu/mathematics-faculty-pubs/62
https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1061&context=mathematics-faculty-pubs
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Institution: Ateneo De Manila University
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Summary:We offer a new and simpler proof of a recent ϵ-δ characterization of Baire class one functions using a theorem by Henri Lebesgue. The proof is more elementary in the sense that it does not use the Baire Category Theorem. Furthermore, the proof requires only that the domain and range be separable metric spaces instead of Polish spaces.