Timeline for Design measure, which cannot be factorized as a product of measures

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Mar 7, 2017 at 17:33	comment	added	Anthony Quas		I just noticed that you posted the exact same question at essentially the same time on math.stackexchange.com. You did the same thing with a previous question. Please don't do this. It leads to wasted effort. If in doubt, post to MSE first. After a few days, if there is no answer, you can post to MO, along with a note that its cross-posted. For reference, this question is probably closer to the MSE level.
Mar 7, 2017 at 17:28	comment	added	Anthony Quas		By the way: a measure is a product measure if and only if the matrix has rank 1. This one has rank $m$.
Mar 7, 2017 at 14:19	comment	added	Anthony Quas		One interesting way to do this is to set $\mu(x_i,y_i)=m$ for $i\le m$, $\mu(x_i,y_j)=0$ for $j\le m$ with $i\ne j$ , and $\mu(x_i,y_j)=1$ for $j>m$.
Mar 7, 2017 at 14:13	comment	added	Anthony Quas		I think what you're asking for is a essentially a non-trivial coupling of the counting measure on $\mathcal X\times\mathcal Y$. This is usually done with probability measures, although it's not essential. If you write the entries as a matrix, you're asking that $\sum_j \mu(x_i,y_j)=n$ and $\sum_i \mu(x_i,y_j)=m$. There are lots of ways to do this: you're satisfying $n+m$ equations in $nm$ variables.
Mar 7, 2017 at 1:59	answer	added	Bjørn Kjos-Hanssen		timeline score: 1
Mar 7, 2017 at 1:37	history	edited	aberdysh	CC BY-SA 3.0	added 31 characters in body
Mar 7, 2017 at 1:20	history	asked	aberdysh	CC BY-SA 3.0