Definition 4.1.6 (Induced $\s$-Algebra).label Let $X$ be a set, $\Si\suf 2^{X}$ be a $\s$-algebra over $X$ and $E\suf X$ then the collection
\begin{align*}\Si_{E}= \curl{A\cap E:A\in\Si}\end{align*}
is the $\s$-algebra on $E$ induced by $\Si$
Definition 4.1.6 (Induced $\s$-Algebra).label Let $X$ be a set, $\Si\suf 2^{X}$ be a $\s$-algebra over $X$ and $E\suf X$ then the collection
is the $\s$-algebra on $E$ induced by $\Si$
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