Strong Derivative and the Essentially Riemann Integral - Calunod, Immanuel D (Archīum Ateneo, 2021)
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 Lebesgue's criterion for Riemann integrability.