In [8] and [9] J. Jarník and J.Kurzweil introduced an integration process (called PU-integral) for real valued functions on an interval of n with the use of suitably regularC-partitions of unity, instead of the usual partitions. The PU-integral is nonabsolutely convergent and in dimension one falls properly in between the Lebesgue and the Kurzweil-Henstock integrals. In [4], without assuming an...