chapter  3
Semicontinuous functions that are not countably continuous
ByGilbert W. Bassett Jr., Roger Koenker
Pages 10

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. Let us recall the formulation of this classical theorem. It is convenient for us to give the formulation in terms of partial functions (cf. Chapter 0). As usual, we denote by the symbol λ $ \lambda $  (= λ 1 $ \lambda _1 $ ) the Lebesgue measure on R (= R 1 $ \mathbf{R}^1 $ ).