ABSTRACT

As was pointed out in Remark 4 of Chapter 5, the existence of absolutely nonmeasurable real-valued functions with respect to the class of all nonzero σ-finite continuous (i.e., diffused) measures on the real line R is not provable within ZFC set theory, so the help of additional set-theoretical assumptions becomes indispensable. Therefore, speaking of such functions, we should enrich ZFC theory by other axioms.