Sentence examples for preserving actions from inspiring English sources

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 use deformation-rigidity theory in the von Neumann algebra framework to study probability measure preserving actions by wreath product groups.

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].

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.

David Wade, a Kerry spokesman, said the senator, like former President Bill Clinton, had supported preserving affirmative action programs, but changing them.

Morphisms in (^{mathbb {k}Gamma }_{mathbb {k}Gamma }mathcal {YD}) are linear maps preserving the action and the grading.

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.

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.

On the ballot initiative front, despite high profile losses on several gay marriage proposals, progressives fared quite well on other social issues including nods to stem cell research in Michigan; protections for abortion in Colorado, South Dakota, and California; and preserving affirmative action in Colorado.

Emily Raimes, an analyst at Moody's Investors Service, said, "We will be closely monitoring the following things: actions the state takes to preserve cash; actions the state takes to close budget gaps and their effect on structural balance; and whether personal income tax receipts come in above or below state forecasts".