What is an example of a field, that is not a $\sigma$-field?
I read a $\sigma$-field requires closure of it's elements (which are sets) under countable unions, countable intersection, and complement; and a field only requires closure under finite unions, finite intersections, and complement.
[Math] an example of a field, that is not a sigma-field
measure-theory
Best Answer
A field is closed under finite operations. For example take the field generated by open sets $(a,b)\in\mathbb{R}$. By definition, this will include all finite intersections, unions, complements, etc of such sets. Then such a field will never contain a single point, say $\{0\}$, since you'd need an infinite intersection of open sets to generate it.