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1) If f ∈ C(Rn) and f has compact support, then f ∈ Lp(Rn) for every 1 ≤ p ≤ ∞.

2) If f ∈ C(Rn), then f ∈ Lp_{loc}(Rn) for every 1 ≤ p < ∞.

(Where C(Rn) is the space of continuous functions on Rn)

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# Continuously smooth functions and Lp space

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