Generalization of Riemann Integral: The Lebesgue Integral - Raut, Janata (Academic Voices: A Multidisciplinary Journal, 2018)
This paper deals principally with the two integrals, namely Riemann integral and Lebesgue integral starting with definitions and their existences. Basically the domain of the Riemann integrable function is different from that of the Lebesgue integrable function. It is found that every upper (lower) Riemann integral is greater than (less than) or equal to every upper (lower) Lebesgue integral. It includes that Lebesgue integral is the generalization of Riemann integral and is the focus of this paper