# weak convergence

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## weak convergence

[′wēk kən′vər·jəns]
(mathematics)
A sequence of elements x1, x2,… from a topological vector space X converges weakly if the sequence ƒ(x1), ƒ(x2),… converges for every continuous linear functional ƒ on X.
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References in periodicals archive ?
Therefore, Lemma 2, Theorem 5.1 of [1] and the continuity of F prove the weak convergence of [P.sub.N,F] to [P.sub.[[zeta].bar]][F.sup.-1] as N [right arrow] [infinity].
For time series generated by independent identically distributed random variables, weak convergence to an extremal process is known to occur.
A mathematics professor at the Higher School of Economics in Moscow offers a thorough presentation of the theory of weak convergence of measures and other types of convergence, making the material more accessible to a broad audience from different backgrounds than a typical graduate mathematics text.
Weak convergence toward equality is evidenced when the horizontal line at unity crosses the 95 and 99% HDRs.
Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mapping and monotone mapping, J.
Thanks to the weak convergence of [u.sub.n] in [H.sup.1.sub.0]([OMEGA]) and the absolute continuity of the integral, there exists [k.aub.0] independent from n such that, for k > [k.sub.0], we have
We assume that the Boltzmann-Grad limit of the initial one-particle (marginal) distribution function [F.sup.0,[epsilon].sub.1] [member of] [L.sup.[infinity].sub.[xi]] ([R.sup.3] x [R.sup.3]) exists in the sense of a weak convergence of the space [L.sup.[infinity].sub.[xi]] ([R.sup.3] x [R.sup.3]), namely,
[14] investigate the Vaserstein bound [15] by using the weak convergence and Strassen- Dudley theorem.
Takahashi, "Weak convergence theorems for maximal monotone operators with nonspreading mappings in a Hilbert space," Cubo: A Mathematical Journal, vol.
When {[x.sub.n]} is a sequence in E, we denote the strong convergence of {[x.sub.n]} to x G [member of] by [x.sub.n] [right arrow] x and the weak convergence by [x.sub.n] [??] x.
The latter is equivalent to the weak convergence of [P.sup.[theta].sub.n]([omega], x) [right arrow] P.

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