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Measurable functions

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If f is measurable and almost everywhere nonzero, show that 1/f is measurable.

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This solution is comprised of a detailed explanation to answer if f is measurable and almost everywhere nonzero, show that 1/f is measurable.

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I am having difficulty integrating exponential. I want to compute the indefinite integral of r`(t)
where r`(t) is the vector <3, -e(^ -t), 0> ...

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