Integrali di Riemann e di Burkill-Cesari

In this paper a slight modification of the Henstock integration process is studied. The difference is that it involves Riemann-type sums ∑(i)f(zi)(bi−ai) such that the pairwise disjoint system {(ai,bi)} is not necessarily a decomposition of the interval I but the set {zi} lies on a fixed set E satisfying the condition |I−E|=0. Whenever f is Lebesgue integrable the process is independent of E and, as in the Henstock case, it converges to the Lebesgue integral. A lemma of real analysis is of independent interest.