ABSTRACT
After introducing the problem, this chapter presents an elementary proof of the main lifting theorem, first for finite and then for decomposable measures. It introduces a topology by the lifting operation in an abstract (decomposable) measure space for a better understanding of the problem. The chapter includes an extension of the lifting map for vector functions. It provides basic problems and preliminaries along with the definitions as well as theorems and proofs. The lifting theorem is established in two stages. First a relatively simple demonstration of the existence result is given in the key finite measure case, following essentially Traynor’s method. Next this is extended to the general case, which actually establishes the equivalence of the existence of a lifting with the strict localizability of the underlying measure space.
