The Poisson formula for groups with hyperbolic properties.
The prevalence of permutations with infinite cycles
A number of recent papers have been devoted to the study of prevalence, a generalization of the property of being of full Haar measure to topological groups which need not have a Haar measure, and the dual concept of shyness. These concepts give a notion of "largeness" which often differs from the category analogue, comeagerness, and may be closer to the intuitive notion of "almost everywhere." In this paper, we consider the group of permutations of natural numbers. Here, in the sense of category,...
The Prime Orbit Theorem for Quasihyperbolic Toral Automorphisms.
The problem of -simple spectrum for ergodic group automorphisms
The product of certain measurable spaces
The property of weak type (p,p) for the Hardy-Littlewood maximal operator and derivation of integrals
The quasi topology associated with a countably subadditive set function
This is a general study of an increasing, countably subadditive set function, called a capacity, and defined on the subsets of a topological space . The principal aim is the study of the “quasi-topological” properties of subsets of , or of numerical functions on , with respect to such a capacity . Analogues are obtained to various important properties of the fine topology in potential theory, notably the quasi Lindelöf principle (Doob), the existence of a fine support (Getoor), and the theorem...
The quasi-sure ratio ergodic theorem
The Radon measures as functionals on Lipschitz functions
The Radon-Nikodym property and convergence of amarts in Frechet spaces
The Radon--Nikodym theorem for reflexive Banach spaces.
The Ramsey sets and related sigma algebras and ideals
The Range of Atomless Group Valued Measures
The range of vector measures into Orlicz spaces
The rate of convergence of iterates of the Frobenius-Perron operator for piecewise monotonic transformations
The rearrangement inequality for the ergodic maximal function.
The reciprocal Dunford–Pettis property of order in projective tensor products
We investigate whether the projective tensor product of two Banach spaces and has the reciprocal Dunford–Pettis property of order , , when and have the respective property.
The recurrence dimension for piecewise monotonic maps of the interval
We investigate a weighted version of Hausdorff dimension introduced by V. Afraimovich, where the weights are determined by recurrence times. We do this for an ergodic invariant measure with positive entropy of a piecewise monotonic transformation on the interval , giving first a local result and proving then a formula for the dimension of the measure in terms of entropy and characteristic exponent. This is later used to give a relation between the dimension of a closed invariant subset and a pressure...
The regular component of a group-valued set function
The return time theorem fails on infinite measure-preserving systems