Weak Mean Equicontinuity for a Countable Discrete Amenable Group Action

A Weak Countable Choice Principle

A weak choice principle is introduced that is implied both by countable choice and by the law of excluded middle. This principle su ces to prove that metric independence is the same as linear independence in an arbitrary normed space over a locally compact eld, and to prove the fundamental theorem of algebra. 1 Bishop's principle Without appeal to the law of excluded middle, Bishop [1, Lemma 7,...

Every Countable Group Has the Weak Rohlin Property

We present a simple proof of the fact that every countable group Γ is weak Rohlin, that is, there is in the Polish space AΓ of measure preserving Γ-actions an action T whose orbit in AΓ under conjugations is dense. In conjunction with earlier results this in turn yields a new characterization of non-Kazhdan groups as those groups which admit such an action T which is also ergodic.

Structural Properties of Inner Amenable Discrete Groups

Amenable Actions and Exactness for Discrete Groups

It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Čech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete groups. In [KW], Kirchberg and Wassermann discussed exactness for groups. A discrete group G is said to be exact if its reduced group C-algebra C λ(G) is exact. Th...

Weak Covering without Countable Closure

The main result of [MiSchSt] is that Theorem 0.1 holds under the additional assumption that card(κ) is countably closed. But often, in applications, countable closure is not available. Theorem 0.1 also builds on the earlier covering theorems of Jensen, Dodd and Jensen, and Mitchell; some of the relevant papers are [DeJe], [DoJe1], [DoJe2], [Mi1], [Mi2], and [Je]. The results for smaller core mo...