Some results on integration of subdifferentials (Q1968742)

Consider two extended-real-valued functions \(f\) and \(g\) defined over a Banach space \(X\). In this paper the following question is addressed: if one supposes that \(\partial f(x)\subset \partial g(x)\) for all \(x\in X\), is it possible to conclude that \(f\) and \(g\) differ only by a constant? The authors provide a positive answer when the subdifferential operator \(\partial\) enjoys a certain number of axioms.