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Results tagged with measure-concentration
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user 12518
1
vote
1
answer
248
views
(Novel?) notion of concentration/dispersion
Consider the measurable space $(\Omega,\mathscr{B})$ endowed with two positive measures: a "volume $\nu$" and a probability measure $\mu$. For example, one might take $\Omega=\mathbb{R}^n$ (with the u …
- 6,541
8
votes
1
answer
604
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Violating the Lebesgue density theorem
Can anyone exhibit a finite-dimensional metric space (preferably, $R^d$) equipped with a measure that does not satisfy the conclusions of the Lebesgue Density Theorem? Such examples exist in infinite- …
- 6,541
4
votes
0
answers
162
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Are sums extremal for subgaussian concentration?
Bobkov and Houdre https://projecteuclid.org/euclid.bj/1178291721
showed that among all $f:R^n\to R$ that are $1$-Lipschitz
with respect to the $\ell_1$ metric,
the variance is maximized by sums. Namel …
- 6,541