Timeline for Hyperreal finitely-additive measure on [0,1) assigning $b-a$ to $[a,b)$ or $(a,b]$ and infinitesimals to singletons
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 27, 2012 at 12:58 | comment | added | Alexander Pruss | I stand corrected about my comment above. I kind of forgot that I also required $\mu((a,b])=b-a$. (My initial thinking about the problem only required $\mu([a,b))=b-a$. I still don't know the answer to that one, either.) | |
| Sep 27, 2012 at 3:36 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Fixed error in comment about rho
|
| Sep 26, 2012 at 22:49 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 22 characters in body
|
| Sep 26, 2012 at 22:46 | comment | added | Joel David Hamkins | Sean, I agree, and I have edited. | |
| Sep 26, 2012 at 22:43 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Simplified the argument via Sean's comment; added 45 characters in body
|
| Sep 26, 2012 at 22:18 | comment | added | Sean Eberhard | Perhaps more simply, if $a<b$ then $$\mu(\lbrace a\rbrace) + (b-a) = \mu(\lbrace a\rbrace\cup(a,b]) = \mu([a,b]) = \mu([a,b)\cup\lbrace b\rbrace) = (b-a) + \mu(\lbrace b\rbrace).$$ | |
| Sep 26, 2012 at 21:51 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |