Timeline for questions from Halmos' "Measure Theory"
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jan 18, 2018 at 0:48 | history | suggested | jeq | CC BY-SA 3.0 |
Copied image to imgur.com, as it was not being displayed because of the new https rule.
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| Jan 17, 2018 at 23:09 | review | Suggested edits | |||
| S Jan 18, 2018 at 0:48 | |||||
| May 12, 2010 at 2:10 | vote | accept | zzzhhh | ||
| May 11, 2010 at 18:49 | comment | added | The Mathemagician | Get Taylor's GENERALIZED THEORY OF FUNCTIONS AND INTEGRATION or Rao's book and a lot of your confusion will disappear. | |
| May 11, 2010 at 17:29 | answer | added | Arturo Magidin | timeline score: 1 | |
| May 11, 2010 at 9:20 | answer | added | zzzhhh | timeline score: 1 | |
| May 11, 2010 at 7:13 | comment | added | Harry Altman | OK, trying again with working markup... Regarding question 2: I think it's being assumed that $f+g$ and $fg$ are actually meaningful. But really this just comes back to question one - if you have $f(x)=\pm\infty$ or $g(x)=\pm\infty$, this is handled separately. The rest of the time, everything is finite and there are no domain problems. | |
| May 11, 2010 at 2:31 | comment | added | Arturo Magidin | Regarding Question 1: Halmos is not saying that the proof of the general case will follow from the finite valued cases; rather, he states clearly that the case in which $f$ or $g$ take infinite values requires an examination "of a small number of cases"; e.g., for $(f+g)(x)=\infty$ to hold, either $f(x)=\infty$, or $g(x)=\infty$; so the inverse image of $\infty$ will just be a union of two measurable sets, etc. After you "throw away" the points where either $f$ or $g$ is $\pm\infty$, it all takes place where there are no problems. Then you check what happens there directly. | |
| May 11, 2010 at 1:52 | history | asked | zzzhhh | CC BY-SA 2.5 |