# Is there notation denoting that one sigma-algebra is sub-sigma-algebra of another?

The question is self-describing.

-
I think this is reasonable: proofwiki.org/wiki/Definition:Sub-Sigma-Algebra. –  Derek Allums Aug 6 '12 at 20:15
@unit3000-21 the same as for sets? –  Artem Oboturov Aug 6 '12 at 20:37
because they are essentially sets –  Artem Oboturov Aug 6 '12 at 20:39
I believe so. This seems to be confirmed in two other books I have. But don't try to generalize "because they are essentially sets," since for groups, you will see $H \leq G$ or but (probably) not $H \subset G$. –  Derek Allums Aug 6 '12 at 20:48
@unit3000-21 By definition it is a collection of subsets of a set stable under finitely many set operations + contains all infinite unions of subsets from it. –  Artem Oboturov Aug 6 '12 at 21:07

Let $\mathcal{F}, \mathcal{G}$ be $\sigma$-algebras, with $\mathcal{F} \subset \mathcal{G}$.
That is, using $\subset$ (to indicate containment as sets), where it is made clear elsewhere (or from context) that the sets in question are $\sigma$-algebras.