Sentence examples for of sufficiently many from inspiring English sources

What makes the use of finite-dimensional techniques possible is the existence of "sufficiently many" finite subequivalence relations of an arbitrary countable measurable equivalence relation.

We prove a concentration inequality which asserts that, under some mild regularity conditions, every random variable defined on the product of sufficiently many probability spaces exhibits pseudorandom behavior.

It was proposed that the existence of sufficiently many meromorphic solutions of finite order would be a strong indicator of integrability of an equation (see [6 8]).

Once the ordinal number-classes are present, the representation of the alephs is not a severe problem, which means that the representation of transfinite numbers amounts to assuring the existence of sufficiently many transfinite ordinal numbers.

However, its applicability was hindered by the lack of sufficiently many grid points to determine all the fictitious values required for high order schemes at the location where the curvature of the interface is relatively large.

While one can always pretend to be a skeptic about what others know, cooperation's problem is not that of refuting skepticism but rather of obtaining sufficient motivation for sufficiently many partners to afford cooperation's rewards in Rousseau's forest and Hume's meadow.

For cooperation to pay, assurance mechanisms must not only reliably govern cooperative cognition, they must do so in synchrony for sufficiently many members of the relevant exchange group for cooperation to pay.

Mott's counter-example can be avoided if one adds to (ii) the requirement that for sufficiently many realizers Rj of A there exist completers with respect to B (see Silverberg 1996 and Earman and Roberts (1999, section 9) for a discussion).

Ideally, this direction would be determined for a sufficiently large amount of data (sufficiently many realizations of of E1, E2, M1, M2) under the Causal Markov Condition; in other words, the direction of the edge would be "identifiable" as a statistical parameter.

The whole domain is governed by a version of the Archimedean principle to the effect that zero is the only quantity incapable of being multiplied sufficiently many times to equal any given quantity.

By announcing a fact already known to every diner, the cook made this fact common knowledge among them, enabling each of them to eventually deduce the condition of his own face after sufficiently many rings of the bell.[4] Does meeting one's obligations to others serve one's self-interest?