  We review a finite-sampling exponential bound due to Serfling and discuss
related exponential bounds for the hypergeometric distribution. We then discuss
how such bounds motivate some new results for two-sample empirical processes.
Our development complements recent results by Wei and Dudley (2011) concerning
exponential bounds for two-sided Kolmogorov - Smirnov statistics by giving
corresponding results for one-sided statistics with emphasis on "adjusted"
inequalities of the type proved originally by Dvoretzky, Kiefer, and Wolfowitz
(1956) and by Massart (1990) for one-sample versions of these statistics.
