On the ergodicity of the covariance function in the case of a plane

The Bessel functions can be represented as a limit of spherical harmonics. This fact serves as a basis for the transition from the covariance function of the gravity field on the sphere to the covariance function in the plane. It is proved that for the limit R→∞ the variance of the empirical covariance function becomes zero so that the famous nonergodicity proof of Lauritzen holds for the sphere but not for the plane.