  Consider informative selection of a sample from a finite population.
Responses are realized as independent and identically distributed (i.i.d.)
random variables with a probability density function (p.d.f.) f, referred to as
the superpopulation model. The selection is informative in the sense that the
sample responses, given that they were selected, are not i.i.d. f. In general,
the informative selection mechanism may induce dependence among the selected
observations. The impact of such dependence on the empirical cumulative
distribution function (c.d.f.) is studied. An asymptotic framework and weak
conditions on the informative selection mechanism are developed under which the
(unweighted) empirical c.d.f. converges uniformly, in $L_2$ and almost surely,
to a weighted version of the superpopulation c.d.f. This yields an analogue of
the Glivenko-Cantelli theorem. A series of examples, motivated by real problems
in surveys and other observational studies, shows that the conditions are
verifiable for specified designs.
