ABSTRACT
When dealing with various problems of real analysis and classical Lebesgue measure theory, working mathematicians often need to use rather delicate settheoretical arguments, facts or statements.
In this context, it can definitely be said that one of the first profound investigations concerning the role of purely set-theoretical and logical approaches to advanced topics of mathematical analysis was done by Sierpin´ski in his remarkable work [232] (unfortunately, we do not know whether this work is translated into English, while a Russian version of [232], with some inessential changes in it, does exist [238]).
