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- Jan 26, 2012

- 995

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**Problem**: Let $X$ a closed subspace of $L^1(\Bbb R)$. We assume that $X\subset \bigcup_{1<p<\infty}L^p(\Bbb R)$. Show that we can find $p_0\in (1,+\infty)$ such that $X\subset L^{p_0}(\Bbb R)$.

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