Related papers: Finite Quasihypermetric Spaces

A marked metric measure space (mmm-space) is a triple (X,r,mu), where (X,r) is a complete and separable metric space and mu is a probability measure on XxI for some Polish space I of possible marks. We study the space of all (equivalence…

Let X be a compact Hausdorff space and M a metric space. E_0(X,M) is the set of f in C(X,M) such that there is a dense set of points x in X with f constant on some neighborhood of x. We describe some general classes of X for which E_0(X,M)…

For a metric space $X$ with a compatible measure $\mu$, Genevois and Tessera defined the Scaling Group of $(X,\mu)$ as the subgroup $\Gamma$ of $\mathbb{R}_{>0}$ of positive real numbers $\gamma$ for which there are quasi-isometries of $X$…

The space of unitary $C_{0}$-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of $\mathbb{R}_{+}$, is known to admit various interesting residual…

We generalize the concept of mutually unbiased bases (MUB) to measurements which are not necessarily described by rank one projectors. As such, these measurements can be a useful tool to study the long standing problem of the existence of…

A construction analogous to that of Godefroy-Kalton for metric spaces allows to embed isometrically, in a canonical way, every quasi-metric space $(X,d)$ to an asymmetric normed space $\mathcal{F}_a(X,d)$ (its quasi-metric free space, also…

Fix a compact metric space $X$ with finite topological dimension. Let $C^{0}(X)$ be the space of continuous maps on $X$ and $ H^{\alpha}(X)$ the space of $\alpha$-H\"older continuous maps on $X$, for $\alpha\in (0,1].$ $H^{1}(X)$ is the…

Let $X$ be a quasi-Banach space of analytic functions in the unit disc and let $q>0$. A finite positive Borel measure $\mu$ in the closed unit disc $\overline{\mathbb{D}}$ is called a $q$-reverse Carleson measure for $X$ if and only if…

Given a metrizable space $X$, let $AM(X)$ be the space of continuous bounded admissible metrics on $X$, which is endowed with the sup-metric. In this paper, we shall investigate the Borel complexity and the complete metrizability of $AM(X)$…

We show in ZF that: (i) Every subcompact metrizable space is completely metrizable, and every completely metrizable space is countably subcompact. (ii) A metrizable space X=(X,T) is countably compact iff it is countably subcompact relative…

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary…

In this paper, we show that the strong embeddability has fibering permanence property and is preserved under the direct limit for the metric space. Moreover, we show the following result: let $G$ is a finitely generated group with a coarse…

Given a metric space $(X,d)$, a set $S\subseteq X$ is called a $k$-\emph{metric generator} for $X$ if any pair of different points of $X$ is distinguished by at least $k$ elements of $S$. A $k$-\emph{metric basis} is a $k$-metric generator…

On a complete, connected, locally compact, non-compact geodesic space $(X,d)$, we assign each compact set a distance-like function. With the help of these functions, we obtain a pseudo-metric on the space of (non-empty) compact subsets of…

For a nonadditive measure $\mu$, the space $\mathcal{L}^0(\mu)$ of all measurable functions, the Choquet-Lorentz space $\mathcal{L}^{p,q}(\mu)$, the Lorentz space of weak type $\mathcal{L}^{p,\infty}(\mu)$, the space…

For a homeomorphism $T$ on a compact metric space $X$, a $T$-invariant Borel probability measure $\mu$ on $X$ and a measure-theoretic quasifactor $\widetilde{\mu}$ of $\mu$, we study the relationship between the local entropy of the system…

The paper deals with the theory of balayage of Radon measures $\mu$ of finite energy on a locally compact space $X$ with respect to a consistent kernel $\kappa$ satisfying the domination principle. Such theory is now specified for the case…

Given a degeneration of compact projective complex manifolds $X$ over the punctured disc, with meromorphic singularities, and a relatively ample line bundle $L$ on $X$, we study spaces of plurisubharmonic metrics on $L$, with particular…

Bochner's theorem says that if $M$ is a compact Riemannian manifold with negative Ricci curvature, then the isometry group $\operatorname{Iso}(M)$ is finite. In this article, we show that if $(X,d,m)$ is a compact metric measure space with…

Considering a finite Borel measure $ \mu $ on $ \mathbb{R}^d $, a pair of conjugate exponents $ p, q $, and a compatible semi-inner product on $ L^p(\mu) $, we introduce $ (p,q) $-Bessel and $ (p,q) $-frame measures as a generalization of…