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Sep 12, 2022 at 21:50 comment added Nawaf Bou-Rabee You’re welcome! I’m also curious if the result holds if only injectivity is assumed.
Sep 12, 2022 at 19:13 vote accept Tom
Sep 12, 2022 at 19:13 comment added Tom Thanks! This basically satisfies my curiosity, so I'll mark it as resolved. One comment is that these references (and work cited-therein by Basu and Khatri (1969)) all assume the function is bijective. It isn't clear to me if this is necessary, and from a quick skim, the authors don't seem to remark on it.
Sep 12, 2022 at 18:41 history answered Nawaf Bou-Rabee CC BY-SA 4.0