Timeline for Characterizing subsets of integrable functions
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 28, 2022 at 0:49 | answer | added | user7868 | timeline score: 2 | |
| Feb 27, 2022 at 21:28 | history | edited | Kacper Kurowski | CC BY-SA 4.0 |
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| Feb 27, 2022 at 21:27 | comment | added | Kacper Kurowski | Right, I will fix that as well | |
| Feb 27, 2022 at 20:40 | comment | added | LSpice | Also, isn't your $S$ valued in $2^{2^{(0, 1)}}$, i.e., sets of subsets of $(0, 1)$? | |
| Feb 27, 2022 at 20:07 | comment | added | Kacper Kurowski | If so, then I will modify the question as per your suggestion | |
| Feb 27, 2022 at 20:06 | history | edited | Kacper Kurowski | CC BY-SA 4.0 |
added 19 characters in body
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| Feb 27, 2022 at 19:51 | comment | added | Dirk Werner | I think the point of diracdeltafunk's comment was to suggest to add ``$A\subseteq (0,1)$ measurable'' in the definition of $S(f)$. | |
| Feb 27, 2022 at 13:52 | comment | added | Kacper Kurowski | By $\int_A | f |\, \mathrm{d}x$ I mean the Lebesgue integral of $| f |$ calculated over subset $A$. Alternatively, $\int_A | f |\, \mathrm{d}x = \int_{(0,1)} | f | \chi_A \, \mathrm{d}x $, where $\chi_A(x)=1$ if $x \in A$ and $0$ otherwise. | |
| Feb 27, 2022 at 2:15 | comment | added | diracdeltafunk | Is the codomain of $S$ really supposed to be the set of Lebesgue-measurable subsets of $(0,1)$? Otherwise how is $\int_A$ meant to be interpreted in the definition of $S(f)$? | |
| Feb 27, 2022 at 1:00 | history | asked | Kacper Kurowski | CC BY-SA 4.0 |