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Revision difference : weak convergence |
| Version 4 |
Version 3 |
| Suppose $X$ is a topological vector space, $X'$ is the continuous dual |
Suppose $X$ is a topological vector space, $X'$ is the continuous dual |
| of $X$, and $x_0,x_1,\ldots $ is a sequence in $X$. |
of $X$, and $x_0,x_1,\ldots $ is a sequence in $X$. |
| Then we say that $x_i$ \emph{converges weakly} to $x\in X$ if |
Then we say that $x_i$ \emph{converges weakly} to $x\in X$ if |
| $$ |
$$ |
| \lim_{i\to \infty} f(x_i) = f(x) |
\lim_{i\to \infty} f(x_i) = f(x) |
| $$ |
$$ |
| for every $f\in X'$. |
for every $f\in X'$. |
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