= Integrable power-law density at an axis or center
{title2=$p>-2\text{ at an axis},\quad p>-3\text{ at a point in three dimensions}$}
A nonnegative <mass density> proportional to $r^p$ has finite local mass near a straight axis if $\int_0^\varepsilon r^{p+1}\,dr$ converges, namely $p>-2$. Near a three-dimensional center the corresponding condition is convergence of $\int_0^\varepsilon r^{p+2}\,dr$, namely $p>-3$. These follow from the <cylindrical volume element> and <spherical volume element>. At equality the divergence is logarithmic. An unbounded density does not by itself imply infinite <mass>.
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