An ergodic theorem without invariant measure
An exact functional Radon-Nikodym theorem for Daniell integrals
Given two positive Daniell integrals I and J, with J absolutely continuous with respect to I, we find sufficient conditions in order to obtain an exact Radon-Nikodym derivative f of J with respect to I. The procedure of obtaining f is constructive.
An example concerning automorphisms of generalized cubes
An example of a weak Bernoulli process which is not finitary
An existence result on partitioning of a measurable space: Pareto optimality and core
This paper investigates the problem of optimal partitioning of a measurable space among a finite number of individuals. We demonstrate the sufficient conditions for the existence of weakly Pareto optimal partitions and for the equivalence between weak Pareto optimality and Pareto optimality. We demonstrate that every weakly Pareto optimal partition is a solution to the problem of maximizing a weighted sum of individual utilities. We also provide sufficient conditions for the existence of core partitions...
An exponential estimate for convolution powers
We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.
An expression of classical dynamics
An Extended Notion of Refinement-Unboundedness.
An extension of Brunovský's Scorza-Dragoni type theorem for unbounded set-valued functions
An Extension of the Daniell Integration Scheme
An extension of the Steinhaus-Weil theorem
An extension theorem for modular measures on effect algebras
We prove an extension theorem for modular measures on lattice ordered effect algebras. This is used to obtain a representation of these measures by the classical ones. With the aid of this theorem we transfer control theorems, Vitali-Hahn-Saks, Nikodým theorems and range theorems to this setting.
An extension to the non-metric case of a theorem of Glasner.
An extension which is relatively twofold mixing but not threefold mixing
We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold.
An semigroup of zero measure which contains a translate of every countable set
An ideal theoretic characterization of finite sets, finite algebras, and -algebras of countably generated type
An improved bound on the Minkowski dimension of Besicovitch sets in .
An incompatibility theorem
An inequality for correlated measurable functions.
An inequality for the Hardy-Littlewood maximal operator with respect to a product of differentiation bases