= Radial profile
{title2=$u(x)=\bar u(|x|)$}
A radial profile is a one-variable function $\bar u$ representing a <radial function> $u$ by $u(x)=\bar u(|x|)$. On an <annulus> $a<|x|<b$, with $a>0$, the <spherical coordinate system> identifies its <Lp norm> with the weighted profile <norm> through $\int|u|^p=|S^{n-1}|\int_a^b|\bar u(r)|^p r^{n-1}\,dr$. Thus equality of two <radial functions> <almost everywhere> identifies their profiles <almost everywhere> in the ordinary one-dimensional sense.
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