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This question seems like an easy measure theory problem but I don't know how to proceed.

Suppose $f$ is defined a.e., and suppose $g$ and $h$ are defined on all $\mathbb R^n$, and $g=f$ a.e. and $h=f$ a.e. Then prove that:

$g$ is measurable $\iff$ $h$ is measurable.

I think this is true if and only if notation is trivial but how to prove?

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    Is this homework? Or rather: are your 5 questions (so far) all parts of a homework?2012-05-06

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