Lebesgue nonmeasurable functions and functions without the Baire property

This chapter is devoted to some well-known constructions of a function acting from real line R into R and nonmeasurable in the Lebesgue sense (respectively, of a function acting from R into R and lacking the Baire property). Obviously, the existence of such a function is equivalent to the existence of a subset of R nonmeasurable in the Lebesgue sense (respectively, of a subset of R without the Baire property). The chapter indicates one important common feature of Lebesgue measurable sets and of sets with the Baire property. It considers one direct construction of a Lebesgue nonmeasurable function acting from R into R. The chapter also includes exercise problems related to Lebesgue nonmeasurable functions.