Summary: The randomness in SRSWR sampling scheme has two components: the choice of distinct units and their repetitions. D. Basu [Sankhyā 20, 287- 294 (1958; Zbl 0088.126)] invoked the notion of sufficiency in this framework showing that the distinct units behave like a sufficient statistics in usual sense. Going one step ahead we can call the repetitions of the distinct units ‘ancillary’ since they do not contain any information about population characteristics. It is shown that the above fact is reflected in an interesting way in the behaviour of empirical processes in large samples. In large samples such a break-up of variability is similar to the celebrated theorem of D. Basu [ibid. 15, 377-380 (1955; Zbl 0068.134)].