Equation 5.8.3A577EADC63E4

\begin{equation} \begin{split} \int _{B(x,r)}F\, \mathrm{d}V_{2n} & =s_{2n-1}\int _{S^{2n-1}}\int _0^ rF(x+\rho a)\rho ^{2n-1}\, \mathrm{d}\rho \, \mathrm{d}\tau (a)\\ & =\frac{s_{2n-1}}{2\pi }\int _{S^{2n-1}}\int _{|t|<r} F(x+ta)|t|^{2n-2}\, \mathrm{d}V_2(t)\, \mathrm{d}\tau (a). \end{split} \end{equation}