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Possible Duplicate:
When $L_p = L_q$?

Can anyone tell me under what condition these two spaces $L^p(\mu)$ and $L^s(\mu)$ contain the same functions?

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    My bet (assuming $p\ne s$): Only when these spaces are finite dimensional, i.e., when the total space is the finite union of atoms.2012-10-25
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    @HaraldHanche-Olsen: It seems that Nate's answer in [When $L_p=L_q$?](http://math.stackexchange.com/q/9692) confirms your bet.2012-10-26
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    @lp-man: Indeed it does. No surprise there.2012-10-26

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