Timeline for Regular measure in a Hausdorff space
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 24, 2021 at 4:10 | review | Close votes | |||
| Feb 5, 2021 at 20:23 | |||||
| Jan 21, 2021 at 17:22 | comment | added | Nate Eldredge | In particular, see math.stackexchange.com/questions/209532/…. If $A \subset \mathbb{R}$ is a set with zero inner Lebesgue measure and nonzero outer Lebesgue measure, there is an extension $\mu'$ of Lebesgue measure to $\beta = \sigma(\mathcal{B} \cup \{A\})$ for which $\mu(A)=0$. But for any open set $U \supset A$ we have $\mu'(U) = m(U) \ge m^*(A) > 0$. | |
| Jan 21, 2021 at 17:17 | comment | added | Nate Eldredge | I see, so you know only that it's inner and outer regular on Borel sets, but you want to know whether the outer regularity also holds on sets $A \in \beta$ which are not necessarily Borel. I don't think it is true. | |
| Jan 21, 2021 at 17:10 | history | edited | evaristegd | CC BY-SA 4.0 |
Add link to post about regular measures
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| Jan 21, 2021 at 17:08 | comment | added | evaristegd | @NateEldredge , thanks for the comment. Regarding the level of the question, I thought it was of a level high enough for MO; however, I'll be more cautious and try MathSE instead next time. Re: regularity, similarly to this post, I define regularity as having both inner regularity and outer regularity. | |
| Jan 21, 2021 at 17:01 | comment | added | Nate Eldredge | I'm not sure whether this is a research-level question; Math.SE might be more suitable. But either way, can you state precisely what you mean by "$\mu$ is regular"? Different authors use different definitions, and for some, the statement you want to prove is literally part of the definition of being regular. | |
| Jan 21, 2021 at 16:32 | review | First posts | |||
| Jan 21, 2021 at 16:36 | |||||
| Jan 21, 2021 at 16:30 | history | asked | evaristegd | CC BY-SA 4.0 |