Timeline for Distributional derivative of non continuously differentiable functions
Current License: CC BY-SA 2.5
4 events
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| Jul 6, 2010 at 16:05 | comment | added | Andrey Rekalo | Thank you for the comment. Well, the functions whose distributional derivatives have an atomic component are excluded by the condition $f'\in L_{loc}(\mathbb R)$. And the functions with singular non-atomic distributional derivatives are ruled out by the second bullet point: $f$ should be absolutely continuous. | |
| Jul 6, 2010 at 15:49 | comment | added | Harald Hanche-Olsen | I think you somewhat misrepresented Lebesgue's decomposition theorem. There are “step functions” with an infinite number of steps, whose distributional derivatives are infinite linear combinations of delta functions – but more seriously, there are functions like the Cantor function en.wikipedia.org/wiki/Cantor_function whose distributional derivatives are singular but non-atomic measures. | |
| Jul 5, 2010 at 17:44 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
added 294 characters in body
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| Jul 5, 2010 at 13:40 | history | answered | Andrey Rekalo | CC BY-SA 2.5 |