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

• Main Authors: Cabral, Emmanuel A, Fenecios, Jonald P
• Format: text
• Published: Archīum Ateneo 2015
• Subjects: Baire class one function; oscillation of a function; Polish spaces; separable metric spaces; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/62; https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1061&context=mathematics-faculty-pubs
• Institution: Ateneo De Manila University

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...