Definition 13.1.8 (Borel $\sigma$-Algebra on $\ol{\real}$). The family
\[\cb_{\ol{\real}}= \bracsn{E \subset \ol \real| E \cap \real \in \cb_\real}\]
is the Borel $\sigma$-algebra on $\ol{\real}$.
Definition 13.1.8 (Borel $\sigma$-Algebra on $\ol{\real}$). The family
is the Borel $\sigma$-algebra on $\ol{\real}$.