Alternative definitions of -density topology
Amarts of finite order and Pettis Cauchy sequences of Bochner integrable functions in locally convex spaces
Amenability, extreme amenability, model-theoretic stability, and dependence property in integral logic
This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove definability of some properties of a topological semigroup such as amenability and the fixed point on compacta property. Second, we define types and develop local stability in the framework of integral logic. For a stable formula ϕ, we prove definability of all complete ϕ-types over models and deduce from this the fundamental...
Amoeba relation and Galois-Tukey connections
An Abelian ergodic theorem
An abstract and generalized approach to the Vitali theorem on nonmeasurable sets
Here we present abstract formulations of two theorems of Solecki which deal with some generalizations of the classical Vitali theorem on nonmeasurable sets in spaces with transformation groups.
An Abstract Approach to Weak Topologies in Spaces of Measures
An addendum to a remark on Slutsky's theorem
An algebraic and logical approach to continuous images
An algebraic formulation of ergodic problems
An algebraic group associated to an ergodic diffeomorphism
An algevraic study of the Kolmogorov entropy
An algorithmic determination of optimal measure from data and some applications.
An almost nowhere Fréchet smooth norm on superreflexive spaces
Every separable infinite-dimensional superreflexive Banach space admits an equivalent norm which is Fréchet differentiable only on an Aronszajn null set.
An Alpern tower independent of a given partition
Given a measure-preserving transformation T of a probability space (X,ℬ,μ) and a finite measurable partition ℙ of X, we show how to construct an Alpern tower of any height whose base is independent of the partition ℙ. That is, given N ∈ ℕ, there exists a Rokhlin tower of height N, with base B and error set E, such that B is independent of ℙ, and TE ⊂ B.
An alternative concept of the n-dimensional measure
An alternative proof of the uniqueness of martingale-coboundary decomposition of strictly stationary processes
P. Samek and D. Volný, in the paper ``Uniqueness of a martingale-coboundary decomposition of a stationary processes" (1992), showed the uniqueness of martingale-coboundary decomposition of strictly stationary processes. The original proof is given by reducing the problem to the ergodic case. In this note we give another proof without such reduction.
An analog of Sard's theorem for -smooth functions of two variables.
An analog of the Marcinkiewicz integral in ergodic theory
An analogue of a result of Carathéodory