ABSTRACT
Luzin’s theorem on the structure of Lebesgue measurable functions acting from R into itself is one of the most fundamental statements in real analysis and has numerous applications. This chapter recalls the formulation of this classical theorem. It presents two lemmas that provide some easy facts concerning extensions of semicontinuous partial functions. According to the lemmas, when a real-valued bounded upper semicontinuous function exists on the classical Cantor set which is not countably continuous, then an analogous function exists on an arbitrary uncountable Polish space.
