Reputation
770
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
4 16
Impact
~14k people reached

  • 0 posts edited
  • 0 helpful flags
  • 8 votes cast
1d
accepted Are convex functions enough to determine a measure?
1d
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!
1d
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.
1d
comment Are convex functions enough to determine a measure?
@ByronSchmuland, what is the analogous functions for $f$ and $g$ in higher dimensions?
1d
comment Are convex functions enough to determine a measure?
So it does work if the measures are compactly supported.
1d
awarded  Popular Question
1d
revised Are convex functions enough to determine a measure?
added 10 characters in body
2d
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.
2d
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
Jul
24
comment Is the boundedness necessary to extend harmonically?
Why are the conditions different between harmonic functions and holomorphic function?
Jul
24
comment Is the boundedness necessary to extend harmonically?
So a priori, you don't need to know $v$ is bounded. As long as $v(z) \leq o(\log |z|)$, it will be still true that $v_\epsilon(z)$ will go to $-\infty$. It is the analysis that forced $v$ to be bounded. That means, the statement can be weakened as: "if $u$ is harmonic in the punctured disk and $u(z) \leq o(\log |z|)$, then $u$ can be extended harmonically at the origin."
Jul
20
revised equation of projection onto hyperplane
edited body
Jul
20
answered equation of projection onto hyperplane
Jul
20
comment Define a relation — with functions and derivatives
Let me just remark that in your case, a relation $D$ on $F$ means $D$ is a relation from $F$ to $F$, or, $D\subset F\times F$. Also, personally I would prefer not to use the words "domain" and "range". "domain" gives people a sense that you need to associate everything in it with something in the range, which is not the case in relation. It also might help if you just run some tests before you jump into the problem. For example, is $x^2 Dx$? Is $e^xDe^x+1$?
Jun
30
comment second fundamental form and connection forms
I guess what the author meant by "orthonormal frame" is orthonormal list of vector fields induced from local parametrization.
Jun
30
awarded  Inquisitive