Geodesic
A Note on a Theorem of Dynkin on Necessary and Sufficient Statistics
Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 347-351

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In his paper "Necessary and sufficient statistics for a family of probability distributions", Dynkin (1951) establishes the important concept of rank for such a family with this conclusion: "If the rank is infinite, then the family has no non-trivial sufficient statistic in any size of sample." His concept of rank is based on a theorem, Theorem 2 described below, which has been pointed out by Brown (1964) to be invalid under its hypotheses. This note shows that Dynkin's Theorem 2 remains valid under its original hypotheses provided that the set (in Dynkin's notation) Δ - S is countable. 
Tan, Peter. A Note on a Theorem of Dynkin on Necessary and Sufficient Statistics. Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 347-351. doi: 10.4153/CMB-1969-046-5
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