Timeline for Understanding Gibbs's inequality
Current License: CC BY-SA 3.0
4 events
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| Feb 25, 2013 at 23:01 | comment | added | Tom Leinster | Nice! Thanks. Nevertheless, the "trick" aspect of it means that it doesn't entirely satisfy me: what I want is to get an intuitive picture in my head which makes the result seem obvious (just as for the isoperimetric inequality). @Noah: I suspect the uniqueness part can't be extended to arbitrary real weights too easily. Indeed, in the introduction to their book Inequalities, Hardy, Littlewood and Pólya comment on this limitation of such rational-approximation arguments. | |
| Feb 25, 2013 at 14:58 | comment | added | Noah Stein | This is a cute argument and does answer the original question. Further, it seems to give uniqueness of the optimum for rational weights as a consequence of uniqueness in the equal weights case. Do you know if there is a way to extend the uniqueness part to arbitrary real weights? | |
| Feb 25, 2013 at 14:49 | history | edited | Noah Stein | CC BY-SA 3.0 |
let's -> lets
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| Feb 25, 2013 at 13:57 | history | answered | David E Speyer | CC BY-SA 3.0 |