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

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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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Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

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Question Posted: Jan 25, 2024 01:03 AM

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

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If we show that u a is an open set it is also a Borel set hence u is ...View the full answer

Measures Integrals And Martingales

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