Question: Show that every continuous function (u: mathbb{R} ightarrow mathbb{R}) is (mathscr{B}(mathbb{R}) / mathscr{B}(mathbb{R}))-measurable. [ check that for continuous functions ({u>alpha}) is an open set.]

Show that every continuous function \(u: \mathbb{R} ightarrow \mathbb{R}\) is \(\mathscr{B}(\mathbb{R}) / \mathscr{B}(\mathbb{R})\)-measurable.

[ check that for continuous functions \(\{u>\alpha\}\) is an open set.]

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