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Let $\mu$ denote a finite Borel measure on $\mathbb{R}$. What are the following limits: $\lim_{t\rightarrow\infty}\int_{\mathbb{R}}f(tx)d\mu(x)$ and $\lim_{t\rightarrow0}\int_{\mathbb{R}}f(tx)d\mu(x)?$ $f$ is a continuous function on $\mathbb{R}$ with compact support here.

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