Denote the pointwise limit of $f_{n}(x)$ as $f(x)$. Define $M_n = sup_{x \ \in E} |f_{n}(x) - f(x)|$. Show that $f_n \to f$ uniformly iff $M_n \to 0$ as $n \to \infty$
Not sure how to start. Any tips would be appreciated!I know I have to show both directions since it is an iff statement.
hint
In the initial definition, You just need replace the condition
$$(\forall x\in E)\;|f_n(x)-f(x)|<\epsilon$$ by its equivalent $$\sup_{x\in E}\{|f_n(x)-f(x)|\}<\epsilon$$