Suppose $0
Is $L^{p_1}(\mu)\cap L^{p_0}(\mu)$ dense in $L^r(\mu)$?
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real-analysis
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1 Answers
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Yes. Simple functions composed of sets with finite measure are dense in $L^r(\mu)$ and are contained in $L^{p_1}(\mu) \cap L^{p_0}(\mu)$.
Depending on your particular measure space (for example, if it is $\mathbb R^n$ with the Lebesgue measure), you may also be able to use continuous compactly supported functions.