We prove that any II1 factor L∞(X)⋊Γ arising from a compact, free, ergodic, probability measure preserving action of a countable group Γ with positive first ℓ2-Betti number, β(2)1>0, has a unique group measure space Cartan subalgebra, up to unitary conjugacy.
However, data concerning the influence of add-back therapies on the fertility preserving action of GnRHa are not available.
We use deformation-rigidity theory in the von Neumann algebra framework to study probability measure preserving actions by wreath product groups.
We exhibit also, for every non-amenable free product of groups, free ergodic probability measure preserving actions whose associated equivalence relation has trivial outer automorphisms group.
We begin by talking about probability measure preserving actions of discrete groups, and introduce the notion of the Group Measure Space construction, or the cross product von Neumann algebra.
We show that every non-amenable free product of groups admits free ergodic probability measure preserving actions which have relative property (T) in the sense of S. Popa (2006) [Pop06, Def. 4.1].
This is in contrast with Mackeyʼs point realization theorem, which asserts that any measure preserving Boolean action of a locally compact second countable group on a separable probability algebra can be realized as an action on the points of the associated probability space.
David Wade, a Kerry spokesman, said the senator, like former President Bill Clinton, had supported preserving affirmative action programs, but changing them.
For those of us who lead colleges and universities, preserving affirmative action without doing more is inadequate.
For any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a "universal" hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of G.
His words echoed those of retired Gen. Colin Powell, who said at the N.A.A.C.P. conference in Atlanta last month that there would be no point in preserving affirmative action programs if black youngsters were not prepared academically or socially to take advantage of them.
