Advances in geometric integration (Q1332577)

This is a survey of recent contributions to the extension of the Lebesgue integral over figures, i.e., finite unions of compact intervals, in order to obtain an integral which provides a Gauss-Green theorem for noncontinuously differentiable vector fields and a change of variable formula with respect to groups of transformations including diffeomorphisms. After an analysis of the Kurzweil-Henstock integral and some of its extensions, an integral satisfying the above requirements is proposed and the existence of multipliers for such an integral is discussed. One can regret that, in such a survey, the bibliography is quite selective.