Timeline for Approximation of general measurable maps by simple functions [closed]
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 11, 2016 at 19:57 | vote | accept | StefanH | ||
| Jun 24, 2015 at 16:47 | comment | added | Johannes Hahn | If $Y$ is a Banach space, then a $f$ that is approximated by these kind of simple functions is sometimes called Bochner-measurable or strongly measurable. A Banach valued $f:X\to Y$ is Bochner measurable iff it measurable and $f(X)$ is separable. | |
| Jun 24, 2015 at 16:43 | history | closed |
Gerald Edgar Stefan Kohl♦ András Bátkai Joonas Ilmavirta Johannes Hahn |
Not suitable for this site | |
| Jun 24, 2015 at 14:59 | answer | added | corserine | timeline score: 1 | |
| Jun 24, 2015 at 14:05 | comment | added | StefanH | Okay, thank you. I thought there would be some research around this question and some non-trivial generalisations, so I posted it here. Sorry if it is a trivial question, tell me if you want me to delete it... | |
| Jun 24, 2015 at 14:00 | comment | added | Gerald Edgar | For $Y$ a topological space, the answer is "no" in general. This is the wrong forum for the question, though. | |
| Jun 24, 2015 at 13:51 | comment | added | StefanH | Yes, thank you, you are right, I forgot that. No, I do not require the domain to be ordered, the most general situation I can think of is to equip $Y$ with a topology such that the sequence $(f_n)$ of simple functions should fulfill $f_n(x) \to f(x)$ for each $x$ (meaning that for each open set $U$ around $f(x)$ there exists an index $N$ such that for $n > N$ we have $f_n(x) \in U$). | |
| Jun 24, 2015 at 13:47 | review | Close votes | |||
| Jun 24, 2015 at 16:43 | |||||
| Jun 24, 2015 at 13:29 | comment | added | Gerald Edgar | What is $Y$? You need some sort of convergence in $Y$ for the question even to make sense. Do you want an "order" convergence as you wrote in the real-valued case? | |
| Jun 24, 2015 at 12:40 | history | edited | StefanH | CC BY-SA 3.0 |
added 50 characters in body
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| Jun 24, 2015 at 11:17 | history | asked | StefanH | CC BY-SA 3.0 |