  We investigate the relationship between ergodicity and asymptotic Gaussianity
of isotropic spherical random fields, in the high-resolution (or
high-frequency) limit. In particular, our results suggest that under a wide
variety of circumstances the two conditions are equivalent, i.e. the sample
angular power spectrum may converge to the population value if and only if the
underlying field is asymptotically Gaussian, in the high frequency sense. These
findings may shed some light on the role of Cosmic Variance in Cosmic Microwave
Background (CMB) radiation data analysis.
