Dynamics via measurability.
Convergence of Series of Translations.
Almost Everywhere Convergence of Series.
Ergodic and Mixing Random Walks on Locally Compact Groups.
Totally-disconnected compact metric groups
Uniformly cyclic vectors
A group acting on a measure space (X,β,λ) may or may not admit a cyclic vector in . This can occur when the acting group is as big as the group of all measure-preserving transformations. But it does not occur, even though there is no cardinality obstruction to it, for the regular action of a group on itself. The connection of cyclic vectors to the uniqueness of invariant means is also discussed.
Invariant Means for the Bounded Measurable Functions on a Non-discrete Locally Compact Group.
The number of extensions of an invariant mean
A Generalization of Folner's Condition.
Restricted continuity and a theorem of Luzin
Let P(X,ℱ) denote the property: For every function f: X × ℝ → ℝ, if f(x,h(x)) is continuous for every h: X → ℝ from ℱ, then f is continuous. We investigate the assumptions of a theorem of Luzin, which states that P(ℝ,ℱ) holds for X = ℝ and ℱ being the class C(X) of all continuous functions from X to ℝ. The question for which topological spaces P(X,C(X)) holds was investigated by Dalbec. Here, we examine P(ℝⁿ,ℱ) for different families ℱ. In particular, we notice that P(ℝⁿ,"C¹") holds, where...
Reverse Inequalities.
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