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epsilon
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How does convergence in $\ell^2$ norm imply convergence in $\ell^\infty$-norm with Lipschitz conditions?
@losif Pinelis: hh you are right. But at last we still need an order of $r_c$ in $h_{r_c}$ right?
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How does convergence in $\ell^2$ norm imply convergence in $\ell^\infty$-norm with Lipschitz conditions?
Thanks so much for the clear answer. I am thinking does it still require a lower bound like $g_r(x)>c'\cdot r^d$ for some constant $c'>0$? Otherwise we can not make sure its minimum over $S$ is greater than zero.
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How does convergence in $\ell^2$ norm imply convergence in $\ell^\infty$-norm with Lipschitz conditions?
@JochenGlueck Yes you are right. Let me edit the question to make it clear.
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