On Borel Fields Over Finite Sets

Szekeres, G.; Binet, F. E.

Ann. Math. Statist., Tome 28 (1957) no. 4, p. 494-498 / Harvested from Project Euclid

Résumé

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

Publié le : 1957-06-14
Classification:

@article{1177706978,
     author = {Szekeres, G. and Binet, F. E.},
     title = {On Borel Fields Over Finite Sets},
     journal = {Ann. Math. Statist.},
     volume = {28},
     number = {4},
     year = {1957},
     pages = { 494-498},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177706978}
}

Szekeres, G.; Binet, F. E. On Borel Fields Over Finite Sets. Ann. Math. Statist., Tome 28 (1957) no. 4, pp.  494-498. http://gdmltest.u-ga.fr/item/1177706978/