A descriptive characterization of the generalized Riemann integral (Q915891)

The author has introduced the notion of AC\({}_{\delta}\) and ACG\({}_{\delta}\) functions using the notion of a finite collection of intervals subordinate to a positive function (as in the definition of a generalized Riemann integral). There are two main results: A function \(f: [a,b]\to R\) is generalized Riemann integrable on [a,b] if and only if there exists an \(ACG_{\delta}\) function F on [a,b] such that \(F'=f\) a.e. on [a,b]; F is \(ACG_{\delta}\) on [a,b] if and only if F is ACG\({}_*\) on [a,b].