All Questions
11 questions
23
votes
2
answers
7k
views
What is a Gaussian measure?
Let $X$ be a topological affine space. A Gaussian measure on $X$ is characterized by the property that its finite-dimensional projections are multivariate Gaussian distributions.
Is there a direct ...
- 8,512
9
votes
1
answer
346
views
Is there a uniform solution of the Ruziewicz problem?
For any integer $n\geq 2$ there is one and only one (up to rescaling) rotation-invariant, finitely-additive measure on the Lebesgue $\sigma$-algebra of $S^n$.
The proof of this statement I'm aware of ...
- 91
9
votes
3
answers
654
views
measure with given push-forwards
Let $X,Y$ be locally compact spaces (in my specific case, they are locally compact groups). Suppose that we are given a measure $\mu$ on $X$ and a finite number of quotient maps $p_1,\ldots,p_n:Y\...
4
votes
1
answer
414
views
Finitely Additive Homogeneous Translation Invariant Measure on $\mathcal{P}(\mathbb{R})$
It is known that there exists a finitely additive translation invariant measure on $\mathbb{R}$ that extends the Lebesgue measure. I.e. a function $m:\mathcal{P}(\mathbb{R}) \rightarrow [0,\infty]$ ...
- 297
4
votes
1
answer
495
views
Weil's Haar measure construction from below
Weil's construction of a Haar measure on a locally compact group rests on approximating a function from above by sums of translates of another function.
I would need to know something similar for an ...
user1688
3
votes
1
answer
361
views
Equivalent definitions of strongly proximal action
Consider the following fragment from the paper "C*-simplicity and the unique trace property for discrete groups" by Breuillard, Kalantar,
Kennedy and Ozawa:
I have two questions:
(1) What ...
- 175
3
votes
1
answer
298
views
Averaging measurable functions over amenable group actions
Let $G$ be an amenable group acting on a space $X$.
Amenability means there is a $G$-invariant mean on $L^\infty(G,{\mathbf R})$.
Given a bounded function $f\colon X\to {\mathbf R}$ one can use the ...
- 10.4k
3
votes
0
answers
115
views
Malliavin-Shavgulidze (type) measures on the group of measure-preserving invertible maps on $\mathbb T$?
The Malliavin-Shavgulidze measures on $\operatorname{Diff}^{1}(I)$ (with $I$ an interval of $\mathbb R$) are defined as the image $W_{\sigma} \circ f^{-1}$ of the Wiener measure $W_{\sigma}$ with ...
- 101
2
votes
1
answer
156
views
Ergodic decomposition - how does restricting measure effect it? (Choquet Theory)
Suppose that $G$ is a discrete countable group and $\mu$ is an IRS (invariant random subgroup) of $G$: $\mu$ is conjugation invariant as a probability measure on the subgroups of $G$.
Since all the $...
- 181
1
vote
0
answers
177
views
Building random homeomorphisms of the torus $\mathbb T^2$
In https://arxiv.org/abs/0912.3423, a family of random homeomorphisms of the circle is constructed. Main Question: Can the construction be generalized to higher space dimensions, e.g. to $\mathbb T^2$?...
- 101
0
votes
0
answers
118
views
A measure on the group of homeomorphisms of $\mathbb T^2$
Let us consider the group of measure-preserving homeomorphisms of $\mathbb T^2$ (with transformations identified if they agree almost
everywhere) called $G[\mathbb T^2, \mathcal L^2]$. We shall ...
- 101