Abstract
Possible ways of formalizing the concept of statistically homogeneous and isotropic curvature fluctuations in general relativity are considered. The straightforward way of constructing this concept, which is borrowed from statistical hydromechanics, is shown to lead to a physically degenerate result: the correlations between the fluctuations do not decrease with increasing distance between the points. It is emphasized that this result is a peculiar analogue of the Schur theorem.
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