All Questions
8 questions
2
votes
1
answer
246
views
Ramsey type property of the Lipschitz constant
The following problem was proposed by Pietro Majer as an extension of an earlier question of mine on Lipschitz functions.
For $f$ a Lipschitz function on $\mathbb R^n$, we denote by
$$\text{Lip}(f, U) ...
- 6,195
3
votes
0
answers
222
views
Sets of finite perimeter: intersection with an half space
I have a question regarding sets of finite perimeter. In particular I'm interested to find
$$\mu_{E \cap H_t}, \label{1}\tag{1}$$
where $E$ is a set of finite perimeter in a generic open set $\Omega \...
- 51
10
votes
1
answer
643
views
Estimation of the Gromov–Wasserstein distance of spheres
Let $(X,d_X,\mu_X)$ and $(Y,d_Y,\mu_Y)$ be two metric measure spaces. A probability measure $\mu$ over $X\times Y$ is called a coupling if $(\pi_1)_\sharp \mu=\mu_X$ and $(\pi_2)_\sharp \mu=\mu_Y$. We ...
- 1,565
2
votes
0
answers
144
views
Lebesgue density theorem for "doubling uniformly covering collections of subsets"
I am looking for a version of Lebesgue density theorem that works when restricting to "good" collections of balls with respect to (not necessarily doubling) metric measure spaces. Specifically
Let $(...
- 2,964
7
votes
2
answers
665
views
Non-separable metric probability space
Let us say a metric probability space $(X,\rho,\mu)$ has property (*) if:
the support of $\mu$ is contained in a separable subspace of $X$.
Questions:
1. Is there a standard name for this property?
...
- 6,541
2
votes
1
answer
1k
views
Doubling metrics, doubling measures, Lebesgue density
As stated in this question,
Lebesgue differentiation theorem holds on locally doubling space?
and proved here,
http://www.math.uiuc.edu/~tyson/595f15lecture2.pdf
the Lebesgue differentiation theorem (...
- 6,541
43
votes
0
answers
820
views
A kaleidoscopic coloring of the plane
Problem. Is there a partition $\mathbb R^2=A\sqcup B$ of the Euclidean plane into two Lebesgue measurable sets such that for any disk $D$ of the unit radius we get $\lambda(A\cap D)=\lambda(B\cap D)=\...
- 41.8k
5
votes
0
answers
258
views
Equidistribution of spheres in $\mathbb{R^2}/\mathbb{Z^2}$
Let $\mathbb{H^2}$ be the hyperbolic upper half place, and let $\Gamma$ be a lattice in $SL(2,\mathbb{R})$ acting on $\mathbb{H^2}$. A proof of the equidistribution of spheres on $\mathbb{H^2/\Gamma}$ ...
- 528