A collection of subsets of a set satisfying:
i) implies ;
ii) implies , .
A -field of sets is a field of sets satisfying in addition
a) , , implies , .
A -field is also sometimes called a Borel field of sets.
Sometimes, an algebra (respectively, a -algebra) of sets is taken to mean a field (respectively, a -field) of sets.
M. Hazewinkel
This text originally appeared in Encyclopaedia of Mathematics - ISBN 1402006098