ABSTRACT

In the present (last) chapter our main goal is to show that well-orderings are either negligible or nonmeasurable with respect to the completions of σ-finite diffused product measures. In addition, several consequences of this fact are discussed in the light of some classical problems formulated by Hilbert, Lebesgue and Luzin. In preceding sections of the book we were partially concerned with questions of similar type (cf., for instance, Chapter 4). Here we would like to envisage this topic in more details.