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Jan 31, 2021 at 17:19 comment added Aryeh Kontorovich FWIW: my cumbersome, roundabout proof follows from Theorem D of Foster-Wyner: deanfoster.net/research/low_limits_entropy.pdf (by contradiction: if a sequence satisfying either of my set of conditions existed, it would be a counter-example to their result).
Jan 31, 2021 at 17:11 history edited Iosif Pinelis CC BY-SA 4.0
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Jan 31, 2021 at 17:10 comment added Aryeh Kontorovich Thank you! I had concluded this from much more roundabout reasons -- but your argument is much slicker!
Jan 31, 2021 at 17:09 vote accept Aryeh Kontorovich
Jan 31, 2021 at 17:09 history edited Iosif Pinelis CC BY-SA 4.0
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Jan 31, 2021 at 17:03 history edited Iosif Pinelis CC BY-SA 4.0
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Jan 31, 2021 at 16:18 comment added Aryeh Kontorovich I now have reason to believe that even the "weakening" is impossible.
Jan 31, 2021 at 16:16 history edited Iosif Pinelis CC BY-SA 4.0
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Jan 31, 2021 at 16:16 comment added Aryeh Kontorovich Ah, I see -- my "weakening" was ambiguous. Fixed.
Jan 31, 2021 at 16:15 comment added Aryeh Kontorovich But what about $H_2(\mu_n)$?
Jan 31, 2021 at 16:10 history answered Iosif Pinelis CC BY-SA 4.0