Hyperbolic measures on infinite dimensional spaces
نویسندگان
چکیده
Localization and dilation procedures are discussed for infinite dimensional α-concave measures on abstract locally convex spaces (following Borell’s hierarchy of hyperbolic measures). MSC 2010 subject classifications: 60B11, 28C20, 60F10.
منابع مشابه
An extension theorem for finite positive measures on surfaces of finite dimensional unit balls in Hilbert spaces
A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...
متن کاملPrevalence: a Translation-invariant “almost Every” on Infinite-dimensional Spaces
We present a measure-theoretic condition for a property to hold “almost everywhere” on an infinite-dimensional vector space, with particular emphasis on function spaces such as C and L. Like the concept of “Lebesgue almost every” on finite-dimensional spaces, our notion of “prevalence” is translation invariant. Instead of using a specific measure on the entire space, we define prevalence in ter...
متن کاملRemarks on the Hyperbolic Geometry of Product Teichmüller Spaces
Let e T be a cross product of n Teichmüller spaces of Fuchsian groups, n > 1. From the properties of Kobayashi metric and from the Royden-Gardiner theorem, e T is a complete hyperbolic manifold. Each two distinct points of e T can be joined by a hyperbolic geodesic segment, which is not in general unique. But when e T is finite dimensional or infinite dimensional of a certain kind, then among a...
متن کاملSRB Measures for Infinite Dimensional Dynamical Systems
We study the existence of SRB measures and their properties for a class of infinite dimensional dynamical systems. We show several results including (i) if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has at least one SRB measure; (ii) if the attractor is uniformly hyperbolic, the system is topological mixing, and the splitting ...
متن کاملApplication of measures of noncompactness to infinite system of linear equations in sequence spaces
G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.
متن کامل