Strong Derivative and the Essentially Riemann Integral
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.
Calunod, I. D., & Garces, I. J. L. (2021). Strong derivative and the essentially Riemann integral. Real Analysis Exchange, 46(1), 233–246. https://doi.org/10.14321/realanalexch.46.1.0233