Strong Derivative and the Essentially Riemann Integral

• Main Authors: Calunod, Immanuel D, Garces, Ian June L
• Format: text
• Published: Archīum Ateneo 2021
• Subjects: strong derivative; Riemann integral; primitive of a Riemann integrable function; essentially Riemann integral; essentially continuous function; essentially bounded function; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/158; https://projecteuclid.org/journals/real-analysis-exchange/volume-46/issue-1/Strong-derivative-and-the-essentially-Riemann-integral/10.14321/realanalexch.46.1.0233.short
• Institution: Ateneo De Manila University

We characterize the primitives of Riemann integrable functions using the concept of strong differentiability. We also introduce the notion of essentially Riemann integrable function and characterize it descriptively using its primitive. We also give a characterization of this function that parallels...