On the descriptive definition of the Burkill approximately continuous integral
In a paper of the reviewer [J. Aust. Math. Soc., Ser. A 35, 236-253 (1983; Zbl 0533.26005)] a class of functions, called \([\text{ACG}_{ap}^*]\) functions was defined; this class was then shown to be identical to the class of primitives of the approximately continuous Perron integral of Burkill, the AP-integral. In this paper an example is given that shows the characterization is incorrect. A function is constructed that is AP-integrable, but the primitive of this function is not \([\text{ACG}_{ap}^*]\). The author points out where the error occurs and says he is working on a correct definition for the class of \([\text{ACG}_{ap}^*]\) functions.
approximately continuous Perron integral of Burkill
scientific article; zbMATH DE number 222106
scientific article