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Problem of the Week #287 - Apr 09, 2019

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Euge

MHB Global Moderator
Staff member
Jun 20, 2014
1,896
Here is this week's POTW:

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Let $X$ be a locally compact Hausdorff space, and let $\mu$ be a Radon measure on $X$. Recall that the complement of the support of $\mu$ is the union of all open subsets of $X$ of $\mu$-measure zero. Show that the support of $\mu$ is the set of all $x\in X$ such that for all compactly supported continuous functions $f : X\to [0,1]$ with $f(x) > 0$, the integral $\int_X f\, d\mu > 0$.


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Remember to read the POTW submission guidelines to find out how to submit your answers!
 
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