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Apr 3, 2021 at 8:56 comment added Dave L Renfro I believe this idea was used by Lebesgue around 1903 in proving that continuous monotone functions are (finitely) differentiable almost everywhere, and subsequently the phrase "Lebesgue chain" was often used. See this google search and this google-books search and this google scholar search. Also, repeat all three searches with "chain of intervals" AND "transfinite".
Apr 2, 2021 at 22:49 comment added Pietro Majer I don’t know -I invented it as a student
Apr 2, 2021 at 21:18 comment added Abdelmalek Abdesselam Very nice! How should I refer to this proof?
Apr 2, 2021 at 21:11 history answered Pietro Majer CC BY-SA 4.0