Sentence examples for the free action from inspiring English sources

We will conclude by presenting and proving the key theorem of this talk: The free action on an $L^\infty $ space is ergodic if and only if the corresponding cross product von Neumann algebra is a factor.

We use a subscript F to denote expectation values with respect to the free action.

In the previous section we have considered quotients ( X = A/G) of a complex torus (A = V / Lambda ) by the free action of a finite group G.

After recalling the basic properties of such classifying spaces, an important class of such varieties is introduced, the one of Bagnera de Franchis varieties, the quotients of an Abelian variety by the free action of a cyclic group.

The strategy is again to split the action (S[x,tilde{x}]= S_{mathrm{F}} + S_{mathrm{I}}), where (S_{mathrm{F}}) is called the "free" action and (S_{mathrm{I}}) is called the "interacting" action.

However, the generating functional can also be evaluated by expanding the exponent around the "free" action given by (S_{mathrm{F}}[x t), tilde{x}(t)]=inttilde{x}(t) G^{-1}(t - t') x(t'),dt,dt').

Describes how this was achieved by the free actions of the two peoples involved.

Are these requirements justified, or are they inappropriate infringements on the free actions of competent individuals?

First, Kant suggests that if we abstract the free actions of individual human subjects and examine them as a whole, we can hope to discover a universally applicable, regular progression toward our ultimate moral goal: freedom.

However, it has been suggested by, for example, Roy Bhaskar (Bhaskar 1979: 44) that this reproduction of institutions is the unintended result of the free actions of institutional actors in institutional settings.

He pointed to the obviousness of the humanity of blacks, and in the hypocrisy of the apologists for slavery in America on this question: why should there be special laws prohibiting the free actions of blacks, such as rebelling against the master or any other white person, if slaves were bestial and incapable of independent, responsible behavior?