Timeline for Is the point-wise limit of simple functions a measurable function?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2022 at 5:46 | history | edited | ABB | CC BY-SA 4.0 |
edited title
|
| Jan 18, 2022 at 22:16 | comment | added | Saúl RM | @PietroMajer I was confused at first too, but I think he means that the function takes values in any set $Y$, not just in $\mathbb{C}$ (although that´s not what people usually mean when they say set-valued). | |
| Jan 18, 2022 at 5:40 | vote | accept | ABB | ||
| Jan 17, 2022 at 21:07 | comment | added | Pietro Majer | In fact the standard definition is actually: simple function=finite range, Borel measurable function=linear combination of characteristic functions of Borel subsets. But where are the set-valued functions? | |
| Jan 17, 2022 at 17:09 | answer | added | John Dawkins | timeline score: 5 | |
| Jan 17, 2022 at 16:22 | comment | added | ABB | @Saúl Rodríguez Martín Thanks, Nice argument. | |
| Jan 17, 2022 at 15:30 | comment | added | Saúl RM | Sorry, I didn´t read correctly. In general the statement seems false, you can take the real line in the cofinite topology, $\mathbb{R}'$, and define the functions $f_n:\mathbb{R}'\to\mathbb{R}'$ by $f_n(x)=n\;\forall x$, and then take as a limit some non measurable function you want (the Borel sets would be the countable sets and their complements, and any function $f:\mathbb{R}'\to\mathbb{R}'$ is a pointwise limit of that sequence). In metric spaces it seems to work though. | |
| Jan 17, 2022 at 15:15 | comment | added | Dieter Kadelka | Your notation is unknown to me. What is the definition of a finite range Borel measurable function? | |
| Jan 17, 2022 at 14:56 | review | Close votes | |||
| Jan 24, 2022 at 3:07 | |||||
| Jan 17, 2022 at 14:39 | comment | added | ABB | The link that you referred does not work for set valued functions. | |
| Jan 17, 2022 at 14:38 | comment | added | ABB | @Saúl Rodríguez Martín, It is concerned with set-valued functions not complex valued! I have no clue to find a proof | |
| Jan 17, 2022 at 14:24 | comment | added | Saúl RM | This question is better suited for MSE, in fact it´s answered here | |
| Jan 17, 2022 at 12:51 | history | undeleted | ABB | ||
| Jan 17, 2022 at 12:49 | history | deleted | ABB | via Vote | |
| Jan 17, 2022 at 12:39 | history | asked | ABB | CC BY-SA 4.0 |