A functional central limit theorem for the partial sums of sorted i.i.d. random variables

Let $(X_i,i\ge 1)$ be a sequence of i.i.d. random variables with values in $[0,1]$, and $f$ be a function such that $\mathrm{‘}E(f(X_1{)}^2)<+\mathrm{\infty }$. We show a functional central limit theorem for the process $t\mapsto \sum_{i=1}^n f(X_i)1_{X_i\leq t}$.