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June, 1957 On Borel Fields Over Finite Sets
G. Szekeres, F. E. Binet
Ann. Math. Statist. 28(2): 494-498 (June, 1957). DOI: 10.1214/aoms/1177706978


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 $$(\beta + 1)^{-1/2} \exp \{n(\beta - 1 + \beta^{-1}) - 1\}\quad \text{where}\quad \beta \exp \beta = n$$.


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G. Szekeres. F. E. Binet. "On Borel Fields Over Finite Sets." Ann. Math. Statist. 28 (2) 494 - 498, June, 1957.


Published: June, 1957
First available in Project Euclid: 27 April 2007

zbMATH: 0078.02003
MathSciNet: MR92850
Digital Object Identifier: 10.1214/aoms/1177706978

Rights: Copyright © 1957 Institute of Mathematical Statistics

Vol.28 • No. 2 • June, 1957
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