Best Power in a Probability Inequality Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Using Mac Shane's LemmaUnifrom Convergence of series of product of two sequencesProving a set of Lipschitz Continuous functions is closedInequality with probabilityShow all sequence of $l^1$ with $|x_n|leq frac1n^2$ is compact.How to prove that events $A_p$ are independent, p is prime?A central limit theorem in renewal theoryChebyshev´s inequality best senseA Maximal Version of Empirical Bernstein InequalityIs it true that $(A, mathcal F_A,mathbb P(.|A))$ is a probability space.
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Best Power in a Probability Inequality
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Using Mac Shane's LemmaUnifrom Convergence of series of product of two sequencesProving a set of Lipschitz Continuous functions is closedInequality with probabilityShow all sequence of $l^1$ with $|x_n|leq frac1n^2$ is compact.How to prove that events $A_p$ are independent, p is prime?A central limit theorem in renewal theoryChebyshev´s inequality best senseA Maximal Version of Empirical Bernstein InequalityIs it true that $(A, mathcal F_A,mathbb P(.|A))$ is a probability space.
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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
$endgroup$
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
$endgroup$
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
$endgroup$
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
real-analysis probability lipschitz-functions spheres haar-measure
edited Apr 1 at 14:19
Yuval
asked Mar 29 at 12:50
YuvalYuval
618
618
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 |
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
1
1
$begingroup$
What is the definition of $G_n, k$?
$endgroup$
– Daniel
Apr 1 at 14:24
$begingroup$
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
$begingroup$
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 |
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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