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0

$begingroup$

Let $f:S^n-1rightarrow mathbbR_+$ be a Lipschitz function. For $1leq kleq n$, define $f_k:G_n,krightarrow mathbbR_+$ by $f(E)=max_xin S^n-1cap Ef(x)$. Let $sigma_k$ denote the Haar probability measure on $G_n,k$, and let $sigma = sigma_1$. For every number $t>0$, one can prove that $sigma(xin S^n-1 s.t. f(x)geq t)leq sigma_k(Ein G_n,k:f_k(E)geq t)$. What is the maximal power $m>0$, such that
$sigma(xin S^n-1 s.t. f(x)geq t)leq (sigma_k(Ein G_n,k:f_k(E)geq t))^m$?

Thanks,
Yuval

real-analysis probability lipschitz-functions spheres haar-measure

share|cite|improve this question

edited Apr 1 at 14:19

Yuval

asked Mar 29 at 12:50

YuvalYuval

618

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What is the definition of $G_n, k$?
  $endgroup$
  – Daniel
  Apr 1 at 14:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is the space of k dimensional subspaces of the n’th dimensional Euclidean space.
  $endgroup$
  – Yuval
  Apr 3 at 3:51
  
  

  
  
  
  

add a comment | 

0

$begingroup$

Let $f:S^n-1rightarrow mathbbR_+$ be a Lipschitz function. For $1leq kleq n$, define $f_k:G_n,krightarrow mathbbR_+$ by $f(E)=max_xin S^n-1cap Ef(x)$. Let $sigma_k$ denote the Haar probability measure on $G_n,k$, and let $sigma = sigma_1$. For every number $t>0$, one can prove that $sigma(xin S^n-1 s.t. f(x)geq t)leq sigma_k(Ein G_n,k:f_k(E)geq t)$. What is the maximal power $m>0$, such that
$sigma(xin S^n-1 s.t. f(x)geq t)leq (sigma_k(Ein G_n,k:f_k(E)geq t))^m$?

Thanks,
Yuval

real-analysis probability lipschitz-functions spheres haar-measure

share|cite|improve this question

edited Apr 1 at 14:19

Yuval

asked Mar 29 at 12:50

YuvalYuval

618

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What is the definition of $G_n, k$?
  $endgroup$
  – Daniel
  Apr 1 at 14:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is the space of k dimensional subspaces of the n’th dimensional Euclidean space.
  $endgroup$
  – Yuval
  Apr 3 at 3:51
  
  

  
  
  
  

add a comment | 

$begingroup$

Let $f:S^n-1rightarrow mathbbR_+$ be a Lipschitz function. For $1leq kleq n$, define $f_k:G_n,krightarrow mathbbR_+$ by $f(E)=max_xin S^n-1cap Ef(x)$. Let $sigma_k$ denote the Haar probability measure on $G_n,k$, and let $sigma = sigma_1$. For every number $t>0$, one can prove that $sigma(xin S^n-1 s.t. f(x)geq t)leq sigma_k(Ein G_n,k:f_k(E)geq t)$. What is the maximal power $m>0$, such that
$sigma(xin S^n-1 s.t. f(x)geq t)leq (sigma_k(Ein G_n,k:f_k(E)geq t))^m$?

Thanks,
Yuval

real-analysis probability lipschitz-functions spheres haar-measure

share|cite|improve this question

edited Apr 1 at 14:19

Yuval

asked Mar 29 at 12:50

YuvalYuval

618

$endgroup$

share|cite|improve this question

edited Apr 1 at 14:19

Yuval

asked Mar 29 at 12:50

YuvalYuval

618

share|cite|improve this question

edited Apr 1 at 14:19

Yuval

asked Mar 29 at 12:50

YuvalYuval

618

asked Mar 29 at 12:50

YuvalYuval

618

asked Mar 29 at 12:50

YuvalYuval

618