Abstract
It is shown that the number of Borel Fields over a set $(S)$ of $n$ elements is equal to the number of equivalence relations within $S$. This number is asymptotically equal to $$(\beta + 1)^{-1/2} \exp \{n(\beta - 1 + \beta^{-1}) - 1\}\quad \text{where}\quad \beta \exp \beta = n$$.
Citation
G. Szekeres. F. E. Binet. "On Borel Fields Over Finite Sets." Ann. Math. Statist. 28 (2) 494 - 498, June, 1957. https://doi.org/10.1214/aoms/1177706978
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