We say f n → f {\displaystyle f_{n}\rightarrow f} in L 1 ( μ ) {\displaystyle L^{1}(\mu )} if ∫ | f n − f | d μ → 0 {\displaystyle \int |f_{n}-f|d\mu \to 0} as n → ∞ {\displaystyle n\to \infty } .
