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Sep 8, 2021 at 13:20 comment added Mira Thanks a lot @Ben McKay for recommending this book.
Sep 8, 2021 at 12:51 comment added Ben McKay The translation invariant density, i.e. the Lebesgue measure of Euclidean space. See J.C. Alvarez Paiva and E. Fernandes, Gelfand Transforms and Crofton Formulas for an introduction to densities. We can say that $v'$ is a translation invariant differential form, so we integrate using it: $dX=v'$.
Sep 8, 2021 at 12:48 history edited Glorfindel CC BY-SA 4.0
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Sep 8, 2021 at 12:31 history asked Mira CC BY-SA 4.0