  The $L^{p,\infty}$ quasi-norm of functions on a measure space can be
characterized in terms of their pairing with normalized characteristic
functions. We generalize this result to the case of the outer $L^{p,\infty}$
quasi-norms for appropriate sizes. This characterization provides an explicit
form for certain implicitly defined quasi-norms appearing in an article of Di
Plinio and Fragkos.
