I've been given an assignment question, where I've been asked to identify [itex] L_P[-n, n] [/itex] as a subpsace of [itex] L_p(\mathbb R) [/itex] in the obvious way. It seems to me though that this may be backwards, as if [itex] f \in L_p( \mathbb R) [/itex] then its p-power should also be integrable on any subspace of [itex] \mathbb R [/itex]. However, a function integrable on [-n,n] may not be p-power integrable on all of R. Do I have this backwards?(adsbygoogle = window.adsbygoogle || []).push({});

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# Lp Subspaces

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