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Reading this paper : https://arxiv.org/pdf/1608.04644.pdf the following term : $$L_\infty$$ is referenced in the context of :

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How is $L_\infty$ pronounced ? Is it just "L infinity" ?

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"Ell infinity" or "Ell sub infinity"; both are fine. In this context, it reads most naturally to me as "Ell zero, ell two, and ell infinity".

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