# $\sigma$-algebra

## Primary tabs

Defines:
generated by
Synonym:
sigma-algebra, sigma algebra, $\sigma$ algebra, Borel structure, $\sigma$-field, sigma-field, sigma field, $\sigma$ field
Type of Math Object:
Definition
Major Section:
Reference

## Mathematics Subject Classification

28A60 Measures on Boolean rings, measure algebras

### question about \sigma-algebra

In relation to Djao's entry \sigma-algebra, \emptyset \in \mathcal{B}(E) appears like a premise. As far as I know, \emptyset \in A \forall A. So, why this one is not redundant?
BTW, in my browser IE6 the entry title looks like [red cross]$\sigma$-algebra, missing the greek letter sigma.

### Re: question about \sigma-algebra

You seem to be confusing membership with inclusion (being a subset of). The empty set is a subset of every set, but it is not, for example, a member of itself.

### Re: question about \sigma-algebra

Hi ratboy,
Yes! Now it is clearer for me why E \in \mathcal{B(E)}.
Thank you!
Pedro