In sampling with replacement from a finite population, the sample mean is known to get a smaller variance if repetitions are deleted before forming the mean. The asymptotic behavior of the variance just mentioned is studied.
"Sampling Distinguishable Elements with Replacement." Ann. Math. Statist. 43 (4) 1329 - 1332, August, 1972. https://doi.org/10.1214/aoms/1177692485