In Chap. 2 we start with some rough introduction to the integration theory for finitely additive measures, since it is not so well known. To this end we summarize material that is widely scattered throughout the book of K.P.S. Bhaskara Rao and M. Bhaskara Rao (Theory of charges - a study of finitely additive measures. Academic Press, London, 1983) and that cannot be found elsewhere in such a compact form. But notice that the given survey is far from providing all the results on integration theory which are required for our subsequent investigation. This material is supplemented by some typical examples and by some new results that are used later. \(\mathit {To\ avoid\ confusion\ let\ us\ say\ that\ we\ use\ the\ notion\ measure\ for\ any\ finitely\ additive\ measure\ while\ }\sigma \mbox{-}\mathit {additivity\ is\ indicated\ by\ the\ notion\ }\sigma \mbox{-}\mathit {measure.\ Moreover\ we\ orient\ our\ terminology\ to\ the\ one\ commonly\ used\ in\ measure\ theory\ and,\ in\ doing\ so,\ we\ substantially\ deviate\ from\ the\ terminology\ used\ in\ the\ underlying\ book\ mentioned\ above.}\)