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Aug 18, 2017 at 1:43 comment added Terry Tao When you convolve Haar probability measure on a (compact) subgroup with itself, you get back the same measure, and this can in fact be used as a definition of such subgroups. If you convolve a Gaussian probability measure with itself, you almost get back the same Gaussian measure, but it has spread out by a factor of $\sqrt{2}$. So Gaussians are in some sense a "$\sqrt{2}$-approximate group".
Aug 17, 2017 at 16:32 comment added Chris Jones How exactly do you see a Gaussian as a subgroup of $\mathbb{R}$?
Sep 28, 2010 at 21:10 vote accept Randy Qian
Sep 28, 2010 at 20:47 history edited Terry Tao CC BY-SA 2.5
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Sep 28, 2010 at 20:39 history answered Terry Tao CC BY-SA 2.5