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Let $\mu$ be a finite positive measure on the borel sets in $\mathbb{R}$ and suppose $\mathcal{L}^{1}(\mathbb{R},\mu) \subset \mathcal{L}^{\infty}(\mathbb{R},\mu)$. Show that there exists $c>0$ such that if A is a Borel set with $\mu(A) > 0$ then $\mu(A) \geq c$.

No idea at all. Can you please help?

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