Local compactness plus uniform tail control

Strong convergence on every bounded region combines with a tail estimate uniform in the sequence to give global strong convergence.

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- Strong convergence from weak convergence and tightness Local compactness plus uniform tail control

Strong convergence from weak convergence and tightness

If local compactness makes every subsequential local limit agree with the global weak limit and the

L^{2}

mass is uniformly tight, weak convergence upgrades to strong convergence.

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