Verify that (mathscr{B}(overline{mathbb{R}})) defined in (8.5) is a (sigma)-algebra. Show that (mathscr{B}(mathbb{R})=mathbb{R} cap mathscr{B}(overline{mathbb{R}})). Equation 8.5 B*

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Verify that \(\mathscr{B}(\overline{\mathbb{R}})\) defined in (8.5) is a \(\sigma\)-algebra. Show that \(\mathscr{B}(\mathbb{R})=\mathbb{R} \cap \mathscr{B}(\overline{\mathbb{R}})\).

Equation 8.5

B* E B(R) B* BUS for some BEB(R) and = SE {0, {-x}, {+0},{-0, +0}} (8.5)

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