Related papers: Moment Measures
We develop a new duality between endomorphisms of measure spaces, on the one hand, and a certain family of positive operators, called transfer operators, acting in spaces of measurable functions on, on the other. A framework of standard…
Let $x$ and $y$ be two unit vectors in a normed plane $\mathbb{R}^2$. We say that $x$ is Birkhoff orthogonal to $y$ if the line through $x$ in the direction $y$ supports the unit disc. A B-measure (Fankh\"anel 2011) is an angular measure…
Characterizations of surjective isometries with respect to the Kuiper distance on three classes of Borel probability measures of $\mathbb{R}$ (or equivalently, probability distribution functions) are presented here. These classes are the…
The Borel map takes a smooth function to its infinite jet of derivatives (at zero). We study the restriction of this map to ultradifferentiable classes of Beurling type in a very general setting which encompasses the classical…
Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…
In the present paper we initiate the study of the Musielak-Orlicz-Brunn-Minkowski theory for convex bodies. In particular, we develop the Musielak-Orlicz-Gauss image problem aiming to characterize the Musielak-Orlicz-Gauss image measure of…
If $X$ is an analytic metric space satisfying a very mild doubling condition, then for any finite Borel measure $\mu$ on $X$ there is a set $N\subseteq X$ such that $\mu(N)>0$, an ultrametric space $Z$ and a Lipschitz bijection $\phi:N\to…
Category-measure duality concerns applications of Baire-category methods that have measure-theoretic analogues. The set-theoretic axiom needed in connection with the Baire category theorem is the Axiom of Dependent Choice DC rather than the…
This paper describes the theory of Minkowski problems for geometric measures in convex geometric analysis. The theory goes back to Minkowski and Aleksandrov and has been developed extensively in recent years. The paper surveys classical and…
The spatially homogeneous Boltzmann equation with hard potentials is considered for measure valued initial data having finite mass and energy. We prove the existence of \emph{weak measure solutions}, with and without angular cutoff on the…
Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…
The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher…
We show that regularizing $(2+1)$-dimensional Minkowski spacetime with a finite-resolution Gaussian probe, analogous to Weyl-Heisenberg (Gabor) signal analysis and related quantization, induces a curved geometry with a topological defect.…
A method to generalize results from Riemannian Geometry to Finsler geometry is presented. We use the method to generalize several results that involve only metric conditions. Between them we show that the topology induced by the Finsler…
Given a convex set $C$ in a real vector space $E$ and two points $x,y\in C$, we investivate which are the possible values for the variation $f(y)-f(x)$, where $f:C\longrightarrow [m,M]$ is a bounded convex function. We then rewrite the…
In convex geometry, the Blaschke surface area measure on the boundary of a convex domain can be interpreted in terms of the complexity of approximating polyhedra. In response to a question raised by D. Barrett, this approach is formulated…
In this paper the notion of modular cone metric space is introduced and some properties of such spaces are investigated. Also we define convex modular cone metric which takes values in CR(Y) where Y is a compact Hausdorff space. Then a…
In this paper, we first define the concept of convexity in G-metric spaces. We then use Mann iterative process in this newly defined convex G-metric space to prove some convergence results for some classes of mappings. In this way, we can…
This paper gives a self-contained introduction to the Hilbert projective metric $\mathcal{H}$ and its fundamental properties, with a particular focus on the space of probability measures. We start by defining the Hilbert pseudo-metric on…
We study Leinster's notion of magnitude for a compact metric space. For a smooth, compact domain $X\subset \mathbb{R}^{2m-1}$, we find geometric significance in the function $\mathcal{M}_X(R) = \mathrm{mag}(R\cdot X)$. The function…