Related papers: A dichotomy for the convex spaces of probability m…

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…

Given a compact space $K$, we denote by $P(K)$ the space of all Radon probability measures on $K$, equipped with the $weak^\ast$ topology inherited from $C(K)^\ast$. For nonmetrizable compacta $K$ even basic properties of $P(K)$ spaces…

We study measures on compact spaces by analyzing the properties of fibers of continuous mappings into 2^omega. We show that if a compact zerodimensional space K carries a measure of uncountable Maharam type, then such a mapping has a…

We construct a compact Hausdorff space $K$ such that the space $P(K)$ of Radon probabiblity measures on $K$ considered with the weak$^*$ topology (induced from the space of continuous functions $C(K)$) is countably tight which is a…

The aim of this paper is to present some properties of Choquet maximal Radon probability measures on compact, convex subsets of Hausdorff, locally convex, topological real vector spaces. Theorem 3.12 is the main result of the paper. While…

We consider the correspondence assigning to every Radon measure on two Tychonoff coordinate spaces the set of probability measures with these marginals. It is proved that this correspondence is continuous.

Let X be a separable Banach space and Y a space which has the Radon-Nikodym property. In this work, we show that L(X, Y) has the Radon-Nikodym property, if L(X, Y) is weakly locally uniformly convex or if L(X, Y) is a weakly compactly gen-…

We prove that a homeomorphism of a compact metric space has an expansive measure \cite{ms} if and only if it has many ones with invariant support. We also study homeomorphisms for which the expansive measures are dense in the space of Borel…

Given positive measures $\nu,\mu$ on an arbitrary measurable space $(\Omega, \mathcal F)$, we construct a sequence of finite partitions $(\pi_n)_n$ of $(\Omega, \mathcal F)$ s.t. $$ \sum_{A\in \pi_n: \mu(A)>0} 1_{A} \frac{\nu(A)}{\mu(A)}…

In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a…

We prove that the functor $\Hat{P}$ of Radon probability measures transforms any open map between completely metrizable spaces into a soft map. This result is applied to establish some properties of Milyutin maps between completely…

It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type p if and only if it is Markov p-convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity…

If $\mu_1,\mu_2,\dots$ are positive measures on a measurable space $(X,\Sigma)$ and $v_1,v_2, \dots$ are elements of a Banach space ${\mathbb E}$ such that $\sum_{n=1}^\infty \|v_n\| \mu_n(X) < \infty$, then $\omega (S)= \sum_{n=1}^\infty…

Consider a measurable space with a finite vector measure. This measure defines a mapping of the $\sigma$-field into a Euclidean space. According to Lyapunov's convexity theorem, the range of this mapping is compact and, if the measure is…

Let $\mathbf{\eta}$ be a positive Radon measure on the space of continuous paths from R into a locally compact Polish space $Y$, and assume that $\mathbf{\eta}$ admits an invariant measure. We explicit conditions on $\mathbf{\eta}$ such…

The paper describes two Borel-measurable functions from a measure space into a locally convex space such that the image measure for each function is Radon but their sum is not Borel-measurable.

We generalize the classical Monge-Kantorovich duality--typically established for tight (Radon) probability measures--to separable Baire probability measures, which are strictly more general than tight measures on completely regular…

We show that if K is Rosenthal compact which can be represented by functions with countably many discontinuities then every Radon measure on K is countably determined. We also present an alternative proof of the result stating that every…

We prove pseudocompactness of a Tychonoff space $X$ and the space $\mathcal{P}(X)$ of Radon probability measures on it with the weak topology under the condition that the Stone-\v{C}ech compactification of the space $\mathcal{P}(X)$ is…

Certain countably and finitely additive measures can be associated to a given nonnegative supermartingale. Under weak assumptions on the underlying probability space, existence and (non)uniqueness results for such measures are proven.