A characterization of \(H_ 1\)-integrable functions. (Q595849)

The second author contributed essentially to the \(H_1\)-integral introduced by Garces and Lee. The \(H_1\)-integral is a sum integral based on the concept \(\delta\)-fine refinements of a given tagged partition of the interval over which the integral is defined. The authors show in the paper how the concept of \(H_1\)-integrability is related to the Henstock-Kurzweil integrability of a function. The additional conditions to Henstock-Kurzweil integrability are given by the property that the function is Baire\(^*\)1. The result is then modified variously. Examples are presented.