Definition talk:Trace Sigma-Algebra

From ProofWiki
Jump to navigation Jump to search

I have a problem with the 4th line in the definition section:

$\Sigma_E := E \cap \Sigma = \left\{{E \cap S: S \in \Sigma}\right\}$

Consider:

$X=\{1,2\}$

and the $\sigma$-algebra on $X$:

$\Sigma = \{\{1,2\},\{1\},\{2\},\varnothing \}$

and the subset of $X$:

$E = \{1\}$

Then we have that:

$E \cap \Sigma = \varnothing$

and

$\left\{{E \cap S: S \in \Sigma}\right\} = \{1\}$

-I hope I'm not just reading it wrong. --Jshflynn (talk) 09:54, 28 September 2012 (UTC)

The notation $E \cap \Sigma$ is meant not to mean actual intersection, but rather the "pointwise intersection" of $E$ with $\Sigma$. As it apparently causes confusion, I'll remove that part. --Lord_Farin (talk) 13:41, 28 September 2012 (UTC)