Category:Trace Sigma-Algebras

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This category contains results about trace $\sigma$-algebras.
Definitions specific to this category can be found in Definitions/Trace Sigma-Algebras.

Let $X$ be a set, and let $\Sigma$ be a $\sigma$-algebra on $X$.

Let $E \subseteq X$ be a subset of $X$.


Then the trace $\sigma$-algebra (of $E$ in $\Sigma$), $\Sigma_E$, is defined as:

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