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Results tagged with fa.functional-analysis
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user 99418
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
5
votes
1
answer
317
views
Gaussian-to-Gaussian transformations are affine a.e.?
Let $\mathcal{G}_n = \{ N(\mu,\Sigma) ; \mu \in \mathbb{R}^n, \Sigma > 0\}$ be the collection of Gaussian distributions on $\mathbb{R}^n$ with full support.
If $f : \mathbb{R}^n \to \mathbb{R}^k$ is m …
- 716
4
votes
"Entropy" proof of Brunn-Minkowski Inequality?
I'm a bit hesitant to resurrect an old post, but as a result of some of the things I worked on recently, I'd like to share a new answer to the question in the title. Hopefully some will find it inte …
- 716
3
votes
Accepted
Transforming two smooth densities to the same density
This is impossible if $f$ is injective, without further assumptions such as bijective, differentiable, etc. Let $Q_1,Q_2$ be probability measures on a measurable space $(\Omega, \mathcal{F})$, and as …
- 716