Timeline for Derivatives of measures of bounded variation on intervals
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 8, 2021 at 12:59 | comment | added | Adriano | @Dirk Yes, exactly. But I am mainly interested in references about operators from type $A$ (closedness, weak*-closedness, etc.) and maybe about results like weak*-density for its domain. | |
| Jan 8, 2021 at 12:52 | comment | added | Dirk | If I see correctly, your $M^1[a,b]$ is exactly $BV[a,b]$ where you interpret the functions in $BV$ as measures by multiplying them with the Lebesgue measure. | |
| Jan 8, 2021 at 12:48 | comment | added | Daniele Tampieri | Perhaps reading this Q&A would be somewhat useful: it describes an old result of of Ivan Petrovskii and Renato Caccioppoli identifying conditions for which $$h(x)=\int\limits_a^x f(t)\mathrm{d}g(t) \quad f,g\in C^0$$ exists, without necessarily requiring $f\in BV$ or $g\in BV$. | |
| Jan 8, 2021 at 10:54 | history | edited | Adriano | CC BY-SA 4.0 |
deleted 15 characters in body
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| Jan 8, 2021 at 10:53 | comment | added | Adriano | You are right! I edited my question, accordingly. | |
| Jan 8, 2021 at 10:53 | history | undeleted | Adriano | ||
| Jan 7, 2021 at 15:42 | history | deleted | Adriano | via Vote | |
| Jan 7, 2021 at 14:52 | comment | added | Dirk | if $f$ is just of bounded variation, then $f'$ is a measure and hence, its not clear to me how to multiply $f'$ with the Lebesgue measure. Put differently: What do you hope to get for $A\mu$ when $f$ is the Heaviside function? | |
| Jan 7, 2021 at 13:14 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Jan 7, 2021 at 12:50 | history | asked | Adriano | CC BY-SA 4.0 |