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Dec 5, 2016 at 16:17 comment added user44143 How is this a problem in calculus of variations? That seems to require a differentiable integrand, and I don't see how to make that fit here.
Dec 3, 2016 at 14:07 history edited Pietro Majer CC BY-SA 3.0
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Oct 5, 2010 at 8:14 comment added Pietro Majer That's a good question (sorry for being late in the answer). I will add some remarks to the question on that. With {0,1}, one finds certain graph theoretic quantities (e.g. independence numbers), that give bounds from below for the case of [0,1] (it is equivalent to take the supremum over the sets $A$ in a finite sigma algebra generated by cubes of size 1/2). However, I do not know the answer for {0,1}; as far as I understand it could be even more difficult.
Oct 5, 2010 at 7:50 comment added Bjørn Kjos-Hanssen Interesting. Do you know the answer to your question if you replace $[0,1]$ by $\{0,1\}$?
Jun 27, 2010 at 14:27 history edited Pietro Majer CC BY-SA 2.5
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Jun 27, 2010 at 9:28 history asked Pietro Majer CC BY-SA 2.5