Surface measure on a sphere
= Surface measure on a sphere
{title2=$d\sigma,\quad\int_{\mathbb S^2}d\sigma=4\pi$}
Surface area is the two-dimensional measure induced on the unit <sphere> in three dimensions. It is invariant under orthogonal rotations. It is not the restriction of ambient three-dimensional <Lebesgue measure>, under which the <sphere> has measure zero. Normalizing by the <sphere> area gives a <probability measure>.