Measure and integration: the basic extension theorems

Abstract

The present article returns to the new foundations of measure and integration due to the author. In this development the basic extension procedures lead from the so-called outer and inner premeasures to their unique maximal extensions. The initial version was for extended real valued set functions. In the sequel we want to achieve a major simplification, in that we develop the procedures—with no loss in the essentials—in the traditional frame of nonnegative set functions. The final section then will obtain an important extension theorem in the inner theories.