Related papers: Effectively closed sets of measures and randomness

In this paper, we construct a class of random measures $\mu^{\mathbf{n}}$ by infinite convolutions. Given infinitely many admissible pairs $\{(N_{k}, B_{k})\}_{k=1}^{\infty}$ and a positive integral sequence…

We present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such…

We study large random dissections of polygons. We consider random dissections of a regular polygon with $n$ sides, which are chosen according to Boltzmann weights in the domain of attraction of a stable law of index $\theta\in(1,2]$. As $n$…

We prove in a direct fashion that a multidimensional probability measure is determinate if the higher dimensional analogue of Carleman's condition is satisfied. In that case, the polynomials, as well as certain proper subspaces of the…

For the iterations of $x\mapsto |x-\theta|$ random functions with Lipschitz number one, we represent the dynamics as a Markov chain and prove its convergence under mild conditions. We also demonstrate that the Wasserstein metric of any two…

Let $X=\{X(t),t\in\mathbb{R}^N\}$ be a random field with values in $\mathbb{R}^d$. For any finite Borel measure $\mu$ and analytic set $E\subset\mathbb{R}^N$, the Hausdorff and packing dimensions of the image measure $\mu_X$ and image set…

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'…

It is shown that if a probability measure $\nu$ is supported on a closed subset of $(0,\infty)$, that is, its support is bounded away from zero, then the free multiplicative convolution of $\nu$ and the semicircle law is absolutely…

This work adresses the question of density of piecewise constant (resp. rigid) functions in the space of vector valued functions with bounded variation (resp. deformation) with respect to the strict convergence. Such an approximation…

The general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first. Motivated by recent work on barycentric maps on spaces of…

A real \alpha is called recursively enumerable ("r.e." for short) if there exists a computable, increasing sequence of rationals which converges to \alpha. It is known that the randomness of an r.e. real \alpha can be characterized in…

Let $f: M\rightarrow M$ be a continuous map on a compact metric space $M$ equipped with a fixed metric $d$, and let $\tau$ be the topology on $M$ induced by $d$. First, we will establish some fundamental properties of the mean Hausdorff…

Let $k \ge 1$ be an integer and $f$ a holomorphic endomorphism of $\mathbb P^k (\mathbb C)$ of algebraic degree $d\geq 2$. We introduce a volume dimension for ergodic $f$-invariant probability measures with strictly positive Lyapunov…

We describe the multifractal nature of random weak Gibbs measures on some class of attractors associated with $C^1$ random dynamics semi-conjugate to a random subshift of finite type. This includes the validity of the multifractal…

We study the "Fourier symmetry" of measures and distributions on the circle, in relation with the size of their supports. The main results of this paper are: (1) A one-side extension of Frostman's theorem, which connects the rate of decay…

We construct a class of homogeneous Cantor-Moran measures with all contraction ratios being reciprocal of integers, and prove that they are pointwise absolutely normal. Our approach relies on methods developed by Davenport, Erd{\H{o}}s, and…

This paper has been withdrawn Any real number $x$ in the unit interval can be expressed as a continued fraction $x=[n_1,...,n_{_N},...]$. Subsets of zero measure are obtained by imposing simple conditions on the $n_{_N}$. By imposing…

Let $X=\bigcup\varphi_{i}X$ be a strongly separated self-affine set in $\mathbb{R}^2$ (or one satisfying the strong open set condition). Under mild non-compactness and irreducibility assumptions on the matrix parts of the $\varphi_{i}$, we…

In this paper we study a p harmonic measure, associated with a positive p harmonic function \hat{u} defined in an open set O, subset of R^n, and vanishing on a portion \Gamma of boundary of O. If p>n we show that this p harmonic measure is…

Let $\mu$ be a Borel probability measure on a compact path-connected metric space $(X, \rho)$ for which there exist constants $c,\beta>1$ such that $\mu(B) \geq c r^{\beta}$ for every open ball $B\subset X$ of radius $r>0$. For a class of…