The paper shows that under very broad conditions the usual theorems concerning the limiting distributions of estimates hold for estimates based on samples selected from finite universes, at random without replacement. It may be remarked that under the same conditions, the same conclusions are true for random sampling from finite universes with replacement, if the universes are permitted to change within the limitations set by condition $W$.
"On the Limiting Distributions of Estimates Based on Samples from Finite Universes." Ann. Math. Statist. 19 (4) 535 - 545, December, 1948. https://doi.org/10.1214/aoms/1177730149