The \(g\)-integral is not rotation invariant (Q1308841)

By giving an example of a function which is \(g\)-integrable [see \textit{W. E. Pfeffer}, Rend. Ist. Mat. Univ. Trieste 23, 263-314 (1991; Zbl 0789.26007)] and not rotation invariant, and because of the fact that the \(g^*\)-integral introduced by Novikov and Pfeffer is invariant with respect to lipeomorphisms, the author shows that the family of \(g^*\)- integrable functions is a proper subset of the family of \(g\)-integrable functions. All those classes of integrals are defined in terms of Riemann sums and regular partitions.