Definition talk:Trace Sigma-Algebra
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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)