I had a quick question concerning the definition of a [itex]\sigma[/itex]-algebra [itex]\mathcal{F}[/itex] over a set [itex]\Omega[/itex]. Most sources I've seen (e.g. http://en.wikipedia.org/wiki/Sigma-algebra ) require that [itex]\Omega[/itex] or the empty set be an element of [itex]\mathcal{F}[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

Is this necessary? I ask because I am looking at "Probability: Theory and Examples" by Durrett, and he does not state that as a requirement. He only requires that an element's complement be in [itex]\mathcal{F}[/itex] and that countable (possibly infinite) unions of elements (in the set) remain in the set. Additionally, he says that [itex]\mathcal{F} \neq \emptyset[/itex], but this does not necessarily imply that the empty set is in [itex]\mathcal{F}[/itex].

So, has Durrett just forgotten to include this? Do his later results assume this requirement? Or is it the case this is an unnecessary requirement?

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# Definition of sigma-algebra

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