  Let $\mu$ be a probability measure on $\mathbb{R}$ with cumulative
distribution function $F$, $(x_{i})_{1}^{n}$ a large i.i.d. sample from $\mu$,
and $F_{n}$ the associated empirical distribution function. The
Glivenko-Cantelli theorem states that with probability 1, $F_{n}$ converges
uniformly to $F$. In so doing it describes the macroscopic structure of
$\{x_{i}\}_{1}^{n}$, however it is insensitive to the position of individual
points. Indeed any subset of $o(n)$ points can be perturbed at will without
disturbing the convergence. We provide several refinements of the
Glivenko-Cantelli theorem which are sensitive not only to the global structure
of the sample but also to individual points. Our main result provides
conditions that guarantee simultaneous concentration of all order statistics.
The example of main interest is the normal distribution.
