## weak

The convergence of the sum on the left is of course a weaker statement than the convergence of (2).

In fact, we shall prove our result under the weaker hypothesis that $W$ is weakly bounded, rather than just bounded, on an infinite subset of $G$.

The weight satisfies a weak type $(1,1)$ estimate.

Then $x_n$ converges weak$^*$ to $x$.

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