Timeline for Is the implication ($f$ is Riemann integrable over $D_1$ and $D_2$) $\Rightarrow $ ($f$ is Riemann integrable over $D=D_1\cup D_2$) true?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 6, 2015 at 15:53 | comment | added | Elliot | I think I have already proved (2) is ture ! The proof is not complex. | |
| Jun 6, 2015 at 6:14 | comment | added | Christian Remling | @Q.L.Kwai: Express $\chi_{D_1\cup D_2}f$ in terms of $\chi_{D_j}f$. | |
| Jun 6, 2015 at 3:11 | comment | added | Elliot | @Christian Remling:My friend,your comments may not make sure (2) is true. $int(D_{1})\cup int(D_{2})\subseteq int(D_{1}\cup D_{2})$ .Maybe some interior points of $D_{k}(k=1,2)$ at which $f$ is contionuous will become the discontionuos points of $f $ on $D_{1}\cup D_{2}$. | |
| Jun 6, 2015 at 1:07 | comment | added | Christian Remling | (2) is true. Use that a function is R integrable precisely if it is bounded and continuous a.e. | |
| Jun 5, 2015 at 2:45 | comment | added | Elliot | @David Roberts: Thanks for your mention. | |
| Jun 5, 2015 at 2:43 | comment | added | David Roberts♦ | Please don't use italic text inside colours inside maths environments for emphasis. Your message is not clearer for using many colours and fonts. | |
| Jun 5, 2015 at 2:41 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
Fixed formatting.
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| Jun 5, 2015 at 2:06 | review | First posts | |||
| Jun 5, 2015 at 2:11 | |||||
| Jun 5, 2015 at 2:03 | history | asked | Elliot | CC BY-SA 3.0 |