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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

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up vote 1 down vote accepted

I have never seen such a notation, per se. The closest I've seen is something like:

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.

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