Related papers: Localizing Weak Convergence in $\boldsymbol{ L_\in…

Assume that $(X_t)_{t\in\Z}$ is a real valued time series admitting a common marginal density $f$ with respect to Lebesgue's measure. Donoho {\it et al.} (1996) propose a near-minimax method based on thresholding wavelets to estimate $f$ on…

Let $(X,d)$ be a compact metric space and $\mu$ a Borel probability on $X$. For each $N\geq 1$ let $d^N_\infty$ be the $\ell_\infty$-product on $X^N$ of copies of $d$, and consider $1$-Lipschitz functions $X^N\to\mathbb{R}$ for…

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…

This article fits in the context of the approach to topological problems in terms of the underlying convergence space structures, and serves as yet another illustration of the power of the method. More specifically, we spell out…

We discuss boundedness and compactness properties of the embedding $M_\Lambda^1\subset L^1(\mu)$, where $M_\Lambda^1$ is the closure of the monomials $x^{\lambda_n}$ in $L1([0,1])$ and $\mu$ is a finite positive Borel measure on the…

A standard finite element method discretizes the stochastic linear Schr\"{o}dinger equation driven by additive noise in the spatial variables. The weak convergence of the resulting approximate solution is analyzed, and it is established…

In this paper, we prove first that the iterates of a mean nonexpansive map defined on a weakly compact, convex set converge weakly to a fixed point in the presence of Opial's property and asymptotic regularity at a point. Next, we prove the…

In this paper we discuss how to define an appropriate notion of weak topology in the Wasserstein space $(\mathcal{P}_2(H),W_2)$ of Borel probability measures with finite quadratic moment on a separable Hilbert space $H$. We will show that…

Using elementary probabilistic methods, in particular a variant of the Weak Law of Large Numbers related to the Bernoulli distribution, we prove that for every infinite compact spaces $K$ and $L$ the product $K\times L$ admits a sequence…

We prove that a homeomorphism f of a compact metric space X satisfies the L-shadowing property if and only if its induced hyperspace homeomorphism also satisfies the L-shadowing property. In the proof, assuming only the L-shadowing…

For a strictly stationary sequence of random variables we derive functional convergence of the joint partial sum and partial maxima process under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The…

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C$^*$-algebra. This implies that the weakly almost periodic functionals on $M(G)$, the measure…

We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…

A companion paper develops a framework in which probability measures are represented by distribution-kernel pairs (T,phi) with T a tempered distribution and phi a Schwartz kernel, so that weak moments of all orders exist unconditionally.…

Let $X$ be a Banach space and $\mu$ a probability measure. A set $K \subseteq L^1(\mu,X)$ is said to be a $\delta\mathcal{S}$-set if it is uniformly integrable and for every $\delta>0$ there is a weakly compact set $W \subseteq X$ such that…

A random vector ${\bf X}$ is weakly stable iff for all $a,b\in \mathbb{R}$ there exists a random variable $\Theta$ such that $a{\bf X}+b{\bf X}'\stackrel{d}{=}{\bf X}\Theta$. This is equivalent (see \cite{MOU}) with the condition that for…

We take under consideration Young measures with densities. The notion of density of a Young measure is introduced and illustrated with examples. It is proved that the density of a Young measure is weakly sequentially closed set. In the case…

We demonstrate a measure theoretical approach to the local regularity of weak supersolutions to elliptic and parabolic equations in divergence form. In the first part, we show that weak supersolutions become lower semicontinuous after…

If $G$ is a locally compact groupoid with a Haar system $\lambda$, then a positive definite function $p$ on $G$ has a form $p(x)=< L(x)\xi(d(x)),\xi(r(x))>$, where $L$ is a representation of $G$ on a Hilbert bundle ${\h}=(G^0,\{H_u\},\mu)$,…

We study pointwise convergence properties of weakly* converging sequences $\{u_i\}_{i \in {\mathbb N}}$ in $\mathrm{BV}({\mathbb R}^n)$. We show that, after passage to a suitable subsequence (not relabeled), we have pointwise convergence…