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Let we have the following functions :

$f(x)=(\sin x)^4$ and $g(x)=(\cos x)^4$

How can I prove that $f$ and $g$ are measurable functions

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closed as off-topic by user223391, user147263, Jonas Meyer, hardmath, Mike Pierce Jul 5 '15 at 1:00

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Mesurable for the Lebesgue measure?

Simple : they are continuous, and you can show that every continuous function is mesurable

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