Questions tagged [choquet-theory]
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Continuous real action on affine functions over a Choquet simplex
Let $K$ be a metrizable Choquet simplex. We define $A=\operatorname{Aff}(K,\mathbb{R})$ as the set of real-valued affine continuous functions. This has both the structure of a real Banach space as ...
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Reference for Choquet-like theorem
While reading a paper, I encountered the following statement:
Let $K$ be a convex compact subset of a locally convex topological vector space. If $\mu \in P(K)$ is a Radon probability measure on $K$, ...
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Characterization of inverse limits of finite-dimensional convex cones
Consider a countable inverse system $C_1\substack{f_1 \\ \leftarrow} C_2 \substack{f_2 \\ \leftarrow} C_3 \substack{f_3 \\ \leftarrow} \ldots$ where the $C_i$ are finite-dimensional convex cones of ...
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On examples of subspaces of $C(X)$ for which state spaces are Choquet Simplices
Let $C(X)$ be the Banach space of all Real valued continuous functions on a compact Hausdorff space $X$. What are examples of uniformly closed subspace $\mathcal{A}$ of $C(X)$ such that $\mathcal{A}$ ...
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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 $...
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Peak sets and Choquet boundary of a function algebra
I have two problems to ask.
Let $A$ be a function algebra of $C(K)$. $t\in K$ is said to be a peak point of $A$ if $\exists~f\in A$ s.t. $|f(t)|=\|f\|$ and $|f(s)|<|f(t)|$ for any $s\neq t$. ...
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Dual of the space of affine functions
Let $M^+(D)$ be the space of all positive measures on a closed convex subset $D$ of a locally convex topological vector space $E$. Two measure $\mu, \nu\in M^+(D)$ one can define a partial ordering $\...
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Characterization of state spaces of Boolean algebras
A state space of a Boolean algebra is a Choquet simplex but not all Choquet simplices can be viewed as state spaces of Boolean algebras. Is it known which Choquet simplices are precisely state spaces ...
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Realizing certain affine functions on Choquet simplices on dimension groups
This is a question that is a bit outside my usual mathematical comfort zone, but I feel like an expert might know the answer.
Recall that a dimension group is an ordered abelian group $G$ with ...
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Norms on $\mathbb{R}^d$ whose linear isometries are the hypercube group
It is a known fact that for any $2\neq p\in[1,\infty]$, the linear isometries for the corresponding norm $\|\cdot\|_p$ on $\mathbb{R}^d$ is the set of all square-matrices with entries in $\{-1,1,0\}$, ...
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SubGROUPs of Banach spaces, when are they dense in a vector subspace?
It’s relatively easy to show that if $J$ is a closed subgroup of a finite-dimensional real Banach space, $B$, then it is a vector subspace iff for all bounded linear functionals $\sigma$ of $B$, $\...
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Is there a non-compact Poulsen simplex?
A Choquet simplex is a closed, convex and metrizable subset of a locally convex Hausdorff topological vector space in which every point is a barycenter of a unique probability measure supported on the ...