Uniform conditional L2 norm
= Uniform conditional L2 norm
{title2=$\|f\|_{2,\infty\mid Y}=\mathrm{ess\,sup}_y\|f\|_y$}
The essential supremum over the base of the <conditional L2 norm>. It may be infinite for a globally square-integrable function. For probability fibers, $\|f\|_2\leq\|f\|_{2,\infty\mid Y}$; the uniform norm controls all fibers outside a null set rather than only their average.