An empirical stochastic process for two-sample problems is defined and its weak convergence studied. The results are based upon an identity which relates the two-sample empirical process to the more usual one-sample empirical process. Based on this identity a relatively simple proof of a Chernoff-Savage theorem is obtained. The $c$-sample analogues of these results are also included.
Ronald Pyke. Galen R. Shorack. "Weak Convergence of a Two-sample Empirical Process and a New Approach to Chernoff-Savage Theorems." Ann. Math. Statist. 39 (3) 755 - 771, June, 1968. https://doi.org/10.1214/aoms/1177698309