INTEGRATION ON MEASURE SPACES WITHOUT CONVENTION

We study an integration theory on general measure spaces without imposing the convention infinity times zero equals zero. Our approach depends upon the premises concerning the countable additivity of the corresponding measure and the fact that the measure of the empty set is zero. An outstanding feature of this approach concerns the fact that all the results obtained in this paper are implied by the Third Littlewood’s principle and a Fundamental Theorem asserting that if a bounded real-valued function defined on a set of finite measure is measurable then it is integrable.