In the wikipedia proof of Mercer's theorem, it says that $$\sum_{i=1}^\infty \lambda_i |e_i(t) e_i(s)| \leq \sup_{x \in [a,b]} |K(x,x)|,$$ implies that the sequence $$ \sum_{i=1}^\infty \lambda_i e_i(t) e_i(s) $$
converges absolutely and uniformly on $[a, b] \times [a, b]$. How does the uniform convergence follow here?