Related papers: A simple Efimov space with sequentially-nice space…

Let $K$ be a convex body in $\mathbb{R}^n$ and $f : \partial K \rightarrow \mathbb{R}_+$ a continuous, strictly positive function with $\int\limits_{\partial K} f(x) d \mu_{\partial K}(x) = 1$. We give an upper bound for the approximation…

We give the construction of an infinite topological space with unusual properties. The space is regular, separable, and connected, but removing any nonempty open set leaves the remainder of the space totally disconnected (in fact, totally…

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…

The paper is concerned with the problem whether a nonseparable Banach space must contain an uncountable set of vectors such that the distances between every two distinct vectors of the set are the same. Such sets are called equilateral. We…

For a compact convex subset $K $ of a locally convex Hausdorff space, a measurement on $A(K)$ is a finite family of positive elements in $A(K)$ normalized to the unit constant $1_K$, where $A(K)$ denotes the set of continuous real affine…

The Bernstein Markov Property, shortly BMP, is an asymptotic quan- titative assumption on the growth of uniform norms of polynomials or rational functions on a compact set with respect to L {\mu} 2 -norms, where {\mu} is a positive finite…

Given a compact metric space (X,d) equipped with a non-atomic, probability measure m and a real, positive decreasing function p we consider a `natural' class of limsup subsets La(p) of X. The classical limsup sets of `well approximable'…

Let $Q$ be a relatively compact subset in a Hilbert space $V$. For a given $\e>0$ let $N(\e,Q)$ be the minimal number of linear measurements, sufficient to reconstruct any $x \in Q$ with the accuracy $\e$. We call $N(\e,Q)$ a sampling…

A set of all symmetric Banach function spaces defined on [0,1] is equipped with the partial order by the relation of continuous inclusion. Properties of symmetric spaces, which do not depend of their position in the ordered structure, are…

Locally compact separable metrizable spaces are characterized among all metrizable spaces as those that admit a cofinal sequence $K_1\subset K_2\subset\cdots$ of compact subsets. Their \v{C}ech cohomology is well-understood due to Petkova's…

In this paper we consider the moduli space of complete, conformally flat metrics on a sphere with k punctures having constant positive Q-curvature and positive scalar curvature. Previous work has shown that such metrics admit an asymptotic…

We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of…

In this article, we will characterize regular points respectively by the local vanishing, positivity of the Ricci curvature and $L^2$-solvability of the $\overline\partial$-equation together with Skoda's theorem for Nadel-Lebesgue…

Solomonoff's central result on induction is that the posterior of a universal semimeasure M converges rapidly and with probability 1 to the true sequence generating posterior mu, if the latter is computable. Hence, M is eligible as a…

Let $C$ be an open cone in a Banach space equipped with the Thompson metric with closure a normal cone. The main result gives sufficient conditions for Borel probability measures $\mu,\nu$ on $C$ with finite first moment for which $\mu\leq…

For a regular compact set $K$ in $C^m$ and a measure $\mu$ on $K$ satisfying the Bernstein-Markov inequality, we consider the ensemble $P_N$ of polynomials of degree $N$, endowed with the Gaussian probability measure induced by $L^2(\mu)$.…

Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow…

We first include a result of the second author showing that the Banach space S is complementably minimal. We then show that every block sequence of the unit vector basis of S has a subsequence which spans a space isomorphic to its square.…

A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…

Let $G$ be a non-amenable countable group. We show that every almost automorphic $G$-action on a compact Hausdorff space, with a maximal equicontinuous factor whose phase space is a Cantor set, admits invariant probability measures (this…