ABSTRACT
This chapter commences the author's investigations of "measures" on abstract sets which in principle may have nothing to do with the Euclidean space. After investigating the general properties of abstract measures, the chapter also introduces and studies an appropriate generalisation of continuous functions, called measurable functions. It defines an appropriate general setting for the axiomatic study of measures. The first concept allows to identify particular collections of sets which behave very nicely in terms of taking unions/intersections/complements of its elements. The next concept which gives a tool allowing to define an outer measure on a subset, which arises from the localisation of another outer measure to the subset. This is done in such a way that it vanishes outside the given set.
