Timeline for Mixtures of log-convex functions are log-convex: a reference
Current License: CC BY-SA 4.0
4 events
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| Jun 27, 2018 at 1:52 | comment | added | Iosif Pinelis | I agree that this limit transition is very routine. Yet, I wanted a reference to a quite ready-to-use statement -- especially because its entire direct proof, known to me, is even simpler than the limit transition argument by itself. | |
| Jun 26, 2018 at 21:44 | comment | added | Fedor Petrov | The pass from the sum to a general mixture is so standard abstract nonsense (the set of log-convex functions is a convex cone closed under pointwise limits and blahblah) that I would not care at all. | |
| Jun 26, 2018 at 15:24 | comment | added | Iosif Pinelis | Thank you for your answer. However, Anosov only proves that the sum of log-convex function is log convex. So, one then also needs a limit transition, however simple, to prove the result for general mixtures. I ended up with giving both a reference to Kingman's paper mentioned elsewhere on this page and a short direct proof, using Hölder's inequality, as was suggested in the question. It indeed appears hard to find a reference for general mixtures! (??) | |
| Jun 24, 2018 at 18:39 | history | answered | Fedor Petrov | CC BY-SA 4.0 |