henryforever14
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 Mar 4 comment Haar measure on the groups SO(n) and SO(n,m) for the nice integration formula displayed in the middle, is there a rigorous proof for it? It might be argued by using the uniqueness of Haar measure. It's certainly true that the RHS is left and right invariant. Normalization is not a problem. But how about regularity? Feb 7 awarded Popular Question Nov 24 awarded Notable Question Nov 23 awarded Popular Question Sep 22 awarded Popular Question Aug 6 comment Curvature of a level set If you want straight lines to be your answer, shouldn't you penalize for the sum of the absolute value of curvature of all points? Aug 1 comment Question about the definition of convergence in measure. The first equality in the second long equation, you are interchanging two limits. This is not always true. Jul 28 accepted Are convex functions enough to determine a measure? Jul 28 comment Are convex functions enough to determine a measure? @ByronSchmuland Thanks! It's a nice argument. Please change the very last measure to $\nu(dx)$. I will then accept your answer. Thanks a lot! Jul 28 comment Are convex functions enough to determine a measure? @ByronSchmuland I am sorry, but is that function still convex? For example, the function $f(x,y)=xy$ should not be convex. Jul 28 comment Are convex functions enough to determine a measure? @ByronSchmuland, what is the analogous functions for $f$ and $g$ in higher dimensions? Jul 28 comment Are convex functions enough to determine a measure? So it does work if the measures are compactly supported. Jul 27 awarded Popular Question Jul 27 revised Are convex functions enough to determine a measure? added 10 characters in body Jul 27 comment Are convex functions enough to determine a measure? didn't realize compact domain would make such a huge difference. Thank you. For your last remark, suppose we are dealing with measures that have compact support, how may one prove convex functions are enough? I suppose it would require some approximation of continuous functions by convex functions that I am not aware of. Jul 27 asked Are convex functions enough to determine a measure? Jul 25 comment Confusion about the definition of reflexive relation @BrianM.Scott Thanks! Edited. Jul 25 revised Confusion about the definition of reflexive relation deleted 140 characters in body Jul 24 awarded Teacher Jul 24 answered Confusion about the definition of reflexive relation