# Tagged Questions

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### Choice of number in the proof the 5-r covering theorem

Why has the number 3 been chosen? I have tried drawing this and it seems wrong (its not). The balls definitely dont seem to be disjoint either. It would seem that if a particular $x$ has $r(x)$ ...
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### Support of regular Borel Measure

This question is elementary and hence might be a duplicate. From Rudin, Real and Complex Analysis, page 57. Let $\mu$ be a regular Borel measure on a compact Hausdorff space $X$: assume $\mu(X)=1$. ...
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### $X$ is locally compact Hausdorff space, $\mu$ is Borel regular measure. How to prove $\mu$ is cover $[0,\mu(A)]$

I mean $X$ is locally compact Hausdorff space, $\mu$ is Borel regular measure, and $\mu(\{x\})=0$. For any subset $A$ with finite measure. How to prove for any $0<b<\mu(A)$, we always can find a ...
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### Is it true that a set is compact iff it is closed, bounded, and has finite measure?

I'm sure that this holds for $\mathbb{R}^n$ and for $L^p$ spaces. Is it true in general?
### is the smallest $\sigma$-algebra containing all compact sets the Borel $\sigma$-algebra
Let $R$ be the smallest $\sigma$-algebra containing all compact sets in $\mathbb R^n$. I know that based on definition the minimal $\sigma$-algebra containing the closed (or open) sets is the Borel ...
Let $X$ be the set of all partitions of $[0,1]$ such that each element of the partition is Lebesgue-measurable. Let $Y$ be the set of all partitions of $[0,1]$ such that each element of the ...