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Oct 3, 2011 at 21:01 comment added Nate Eldredge Ok, good counterexample.
Oct 3, 2011 at 19:51 comment added user12713 Thanks for the preliminary reply. I will wait for your full reply. Your ideas seem promising at least. However, one note about linear combinations of probability measures: If $X=\lbrace a, b, c\rbrace$, $p = (1/3,1/3,1/3), q = (1/4,1/4,1/2), r = (0,0,1) \in \Delta(X)$. $r = -3p + 4q$. There cannot exist an $a \in [0,1]$ such that $r= ap +(1-a)q$.
Oct 3, 2011 at 18:20 history answered Nate Eldredge CC BY-SA 3.0