Related papers: A normal measure on a compact connected space

In this paper we propose a method to construct probability measures on the space of convex bodies with a given pushforward distribution. Concretely we show that there is a measure on the metric space of centrally symmetric convex bodies,…

In this paper we construct a metric on the space of idempotent probability measures on the given compactum, which is an idempotent analog of the Kantorovich metric on the space of probability measures.

In this paper we introduce a metrics on the space of idempotent probability measures on a given compactum, which extends the metrics on the compactum. It is proven the introduced metrics generates the pointwise convergence topology on the…

We compute the compactly supported cohomology of the standard realization of any locally finite building.

Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the metric. Then we construct a doubling metric for which the measure of a dillated ball is closely related to these dimensions.

A characterization is presented of barycenters of the Radon probability measures supported on a closed convex subset of a given space. A case of particular interest is studied, where the underlying space is itself the space of finite signed…

We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…

We construct a probability measure $\mu$ supported on a set of zero $2d/p$-Hausdorff measure such that $\hat{\mu}\in L_{p}(\mathbb{R}^d)$.

A simple construction is given of a class of Euclidean invariant, reflection positive measures on a compactification of the space of distributions. An unusual feature is that the regularizations used are not reflection positive.

We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space $S=\Gamma\backslash G/K$ is compact. More precisely, given a sequence of homogeneous probability…

We initiate a systematic investigation of group actions on compact medain algebras via the corresponding dynamics on their spaces of measures. We show that a probability measure which is invariant under a natural push forward operation must…

Let $M$ be a compact 1-manifold. Given a continuous function $g:M\to \mathbb R_+$ we consider the following ordinary differential equation: $\|\dot{f}(t)\|=g(t)$, where $f:M\to \mathbb R^2$. We construct a probability measure on the space…

We give necessary and sufficient conditions for both square integrability and smoothness for densities of a probability measure on a compact connected Lie group.

We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…

In the work it is shown that the space of idempotent probability measures with compact supports is kappa-metrizable if the given Tychonoff space is kappa-metrizable. It is constructed a series of max-plus-convex subfunctors of the functor…

In this work we provide a way to introduce a probability measure on the space of minimal fillings of finite additive metric spaces as well as an algorithm for its computation. The values of probability, got from the analytical solution,…

We obtain a partial converse of Vershik's description of ergodic probability measures on a compact metric space with respect to an isometric action by an inductively compact group. This allows us to identify, in this setting, the set of…

In this paper we investigate algorithmic randomness on more general spaces than the Cantor space, namely computable metric spaces. To do this, we first develop a unified framework allowing computations with probability measures. We show…

We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.

In this paper we will give two different natural generalizations of compact spaces and connected spaces simultaneously. We will show that these generalizations coincide for the subspaces of the real line and that they differ for subspaces…