Let ( Ω , A , μ ) {\displaystyle (\Omega ,{\mathcal {A}},\mu )} be a measure space, 1 ≤ p < ∞ {\displaystyle 1\leq p<\infty } a real number and ( f n ) {\displaystyle (f_{n})} a sequence of A {\displaystyle {\mathcal {A}}} -measurable functions f n : Ω → C ∪ { ∞ } {\displaystyle f_{n}:\Omega \to \mathbb {C} \cup \{\infty \}} .