A Riemann-type integral on a measure space (Q1772949)

For real functions defined on a compact Hausdorff space the (partition of unity) (PU)-integral as well as its non-absolutely variant called the (PU)*-integral are defined. These concepts are based on the notion of PU-partitions and PU*-partitions for which it is assumed that the tags belong to the support of the functions determining the partition. The fundamental properties of the (PU)*-integral are presented and by an example it is shown that there is a (PU)*-integrable function which is not absolutely integrable.