The origin and developments of Kurzweil's generalized Riemann integral
The paper describes to origin and motivation of Kurzweil in introducing a Riemann-type definition for generalized Perron integrals and his further contributions to the topics.
The paper describes to origin and motivation of Kurzweil in introducing a Riemann-type definition for generalized Perron integrals and his further contributions to the topics.
Among the many characterizations of the class of Baire one, Darboux real-valued functions of one real variable, the 1907 characterization of Young and the 1997 characterization of Agronsky, Ceder, and Pearson are particularly intriguing in that they yield interesting classes of functions when interpreted in the two-variable setting. We examine the relationship between these two subclasses of the real-valued Baire one defined on the unit square.