ABSTRACT
In this chapter we would like to analyze Sierpin´ski’s example of a real-valued Lebesgue measurable function on R which is not bounded from above by any real-valued Borel function onR. As Sierpin´ski indicates in his important and extensive article [232], the question of the existence of such a real-valued Lebesgue measurable function was raised by Luzin. In this context, several other realvalued step functions on R with analogous or somewhat similar properties will be discussed below.
