re-reading Halmos (1946)

Based on a (basic) question on X validated, I re-read Halmos‘ (1946) famous paper on the non-existence of centred moments of order larger than the sample size. While the exposition may sound a wee bit daunting, the reasoning is essentially based on a recursion and the binomial theorem, since expanding the kth power leads to lesser moments, all of which can be estimated from a subsample.