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  • 0 posts edited
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  • 9 votes cast
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?
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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