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

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