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.
Borel measures and integration
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real-analysis
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2What do you think they are? On what do you think they will depend? – 2011-08-06