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weak convergence
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(Definition)
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Suppose $X$ is a topological vector space, $X'$ is the continuous dual of $X$ , and $x_0,x_1,\ldots $ is a sequence in $X$ . Then we say that $x_i$ converges weakly to $x\in X$ if $$ \lim_{i\to \infty} f(x_i) = f(x) $$ for every $f\in X'$ . The notation for this is $x_i \xrightarrow[]{w} x$ .
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"weak convergence" is owned by matte.
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Cross-references: converges, sequence, continuous dual, topological vector space
There are 2 references to this entry.
This is version 5 of weak convergence, born on 2005-02-07, modified 2005-02-11.
Object id is 6723, canonical name is WeakConvergence.
Accessed 5011 times total.
Classification:
| AMS MSC: | 46-00 (Functional analysis :: General reference works ) |
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Pending Errata and Addenda
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