# Set inclusion involving the set of locally integrable functions [duplicate]

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Let $0 <p < q < \infty$. Why exactly does the inclusion $L_{\mathrm{loc}}^q(\mathbb{R}^n) \subseteq L_{\mathrm{loc}}^p(\mathbb{R}^n)$ hold?

For clarification:

## marked as duplicate by user296602, Shailesh, Cyclohexanol., user99914, Hans EnglerAug 22 '16 at 1:43

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• Holder's inequality. – user296602 Aug 21 '16 at 21:16
• This might be similar math.stackexchange.com/questions/66029/… – iamvegan Aug 21 '16 at 21:21
• Thanks a lot. I totally forgot the regularity of the Lebesgue measure. – TheGeekGreek Aug 28 '16 at 9:31