Such an axiom is certainly sufficient; assume that a0 is the set of natural numbers {0, 1, 2, …}, and now assume that to each number n is associated an an with power ℵn.
Then the sequence { x n } converges strongly to p ∈ F if and only if lim inf n → ∞ d ( x n, F ) = 0. Proof If { x n } converges to p ∈ F, then lim n → ∞ d ( x n, p ) = 0. Since 0 ≤ d ( x n, F ) ≤ d ( x n, p ), we have lim inf n → ∞ d ( x n, F ) = 0. To prove that the condition is also sufficient, assume that lim inf n → ∞ d ( x n, F ) = 0.
Subsequently, this result was extended in 1969 by Boyd and Wong [2] by weakening the hypothesis on ϕ, in the sense that it is sufficient to assume that ϕ is right upper semi-continuous (not necessarily monotone).
Computer-aided detection marking is a necessary condition, though not sufficient, to assume that CAD has contributed to increased sensitivity or reduced specificity.
Indeed, let us put r : = r D ( f ) (the assertion is, of course, true for any non-negative vector r, but the present formulation is sufficient for our purposes) and assume that, on the contrary, inclusion (6.23) does not hold.
We assume that given sufficient source material, the more common ordering in-text will be the 'correct' (applicable) one.
A necessary condition for a constrained maximum (and also a sufficient one assuming that G is bounded with a single optimum) is provided by the method of Lagrange multipliers, and the Karush Kuhn Tucker conditions.
A 2-tailed Chi square test (α = 0.05 and ß = 0.20) gave a minimum enrolment of 120 patients in each arm for the study to have sufficient power, assuming that the intervention arm would reduce the number of patients having at least 1 of admission medication discrepancy related to home medication by 50%.
"The truth is that we cannot just assume that trust is sufficient," said Jean Pisani-Ferry, director of Bruegel, a research institute.
"The truth is that we cannot just assume that trust is sufficient," said Jean Pisani-Ferry, director of Bruegel, a research institute in Brussels.
