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May 7, 2020 at 14:57 comment added leo monsaingeon I should mention that log-concavity plays absolutely no role here (as should be clear from my answer above). Unless you're working in a finite space $L^p$ and $L^q$ norms cannot be equivalent. Ever.
Apr 7, 2020 at 13:07 history edited leo monsaingeon CC BY-SA 4.0
added 285 characters in body
Apr 7, 2020 at 12:54 history answered leo monsaingeon CC BY-SA 4.0