sentences:  Let "x" be a point in "U" and "r" > 0 be such that the closed ball "B"("x", "r") of center "x" and radius "r" is contained in "U".The spherical mean over the sphere of radius "r" centered at "x" is defined as
  
  where ∂"B"("x", "r") is the ("n"−1)-sphere forming the boundary of "B"("x", "r"), d"S" denotes integration with respect to spherical measure and "ω""n"−1("r") is the "surface area" of this ("n"−1)-sphere.Equivalently, the spherical mean is given by
  
  where "ω""n"−1 is the area of the ("n"−1)-sphere of radius 1.