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Dec 19, 2015 at 20:30 history edited Dr. Wolfgang Hintze CC BY-SA 3.0
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Dec 19, 2015 at 13:12 comment added Dr. Wolfgang Hintze Thank you. Yes, I was aware of it, but considered the contrary case to be trivial. I have now included it in my answer.
Dec 19, 2015 at 13:09 history edited Dr. Wolfgang Hintze CC BY-SA 3.0
Case a (not all $P_j$ are positive)
Dec 19, 2015 at 2:33 comment added dxiv Your premise $P_j > 0$ is stronger than the stated $P_i \ge 0$.
Dec 18, 2015 at 11:28 history edited Dr. Wolfgang Hintze CC BY-SA 3.0
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Dec 18, 2015 at 11:21 history edited Dr. Wolfgang Hintze CC BY-SA 3.0
added 47 characters in body
Dec 18, 2015 at 11:16 history answered Dr. Wolfgang Hintze CC BY-SA 3.0