Timeline for Time-derivative of integral over sub-level set $s(t) := \int_{f^{-1}((-\infty,t])}p(x)dx$
Current License: CC BY-SA 4.0
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| Mar 24, 2022 at 10:58 | comment | added | memorial | In the 60´s of the last century, a number of mathematicians addressed the task of providing an elementary approach to distributions (i.e., without using sophisticated duality theory for special classes of locally convex spaces). Probably the most useful presentation of this theory, and the one most relevant for your question, was given by J. Sebastiao e Silva. This used to be rather inaccessible but is now easily available online. Go to the site jss100.campus.ciencias.ulisboa.pt, then to publicacoes, Textos didaticos and you will find III.1. Theory of distributions. | |
| Mar 22, 2022 at 22:37 | vote | accept | dohmatob | ||
| Mar 22, 2022 at 22:36 | comment | added | dohmatob | Thanks for your input (upvoted). I'm accepted since it appears to be the best answer at the moment. I'd be grateful if you would include any specific references (and not maybe, say, some general monograph on the theory of distributions). | |
| Mar 5, 2022 at 12:40 | history | answered | memorial | CC BY-SA 4.0 |