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We reconsider the issue of proving large-scale spatial homogeneity of the Universe, given isotropic observations about us and the possibility of source evolution in both numbers and luminosities. Two theorems make precise the freedom available in constructing cosmological models that will fit the observations. They make it quite clear that homogeneity cannot be proven without either a fully determinate theory of source evolution, or availability of distance measures that are independent of source evolution. We contrast this goal with the standard approach that assumes spatial homogeneity a priori, and determines source evolution functions on the basis of this assumption.
Mustapha et al. (Mon,) studied this question.