\mu\{|F-G|\geq \varepsilon\}\leq \underbrace{\mu\{|F-F_n|\geq \frac{\varepsilon}{3}\}}_{\rightarrow 0, \text{ kada }n\rightarrow \infty}+\underbrace{\mu\{|F_n-G_n|\geq \frac{\varepsilon}{3}\}}_{=0,\text{ jer } F_n=G_n~\mu \text{ s.s. }~\forall n}+\underbrace{\mu\{|G-G_n|\geq \frac{\varepsilon}{3}\}}_{\rightarrow 0, \text{ kada }n\rightarrow \infty}=0