ABSTRACT
Let λ denote, as usual, the standard Lebesgue measure on the real line R. In preceding sections of this book, we have repeatedly mentioned that there are subsets of R nonmeasurable with respect to λ and that many works were devoted to various constructions of such pathological sets in R (see especially [24], [27], [30], [31], [32], [63], [71], [98], [128], [168], [184], [216], [232], [239], [252], [262]). Of course, the list of references to constructions of this kind can be significantly continued and expanded. Here we would like to begin with making some remarks in connection with the relatively recent paper by Reclaw [216], in which the following statement is established.
