Measure and integration: the basic extension and representation theorems in terms of new inner and outer envelopes (Q2252917)

In his books [Measure and integration. An advanced course in basic procedures and applications. Berlin: Springer (1997; Zbl 0887.28001)] and [Measure and integration. Publications 1997--2011. Basel: Birkhäuser (2012; Zbl 1267.28001)] the author has developed a new approach to measure and integration theory based on new inner and outer envelope formations for isotone \([0,+\infty]\)-set functions. The present paper shows the power of this approach with the example of extension and representation theorems for set functions and functionals. This paper also contains a further development of the final representation theories.