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First it is argued that the density matrix for microcanonical will be diagonal with all diagonal elements equal in the energy representation. Then it is said that this general form should remain the same in all representations. i.e all the off diagonal elements zero and the diagonal elements all equal to one another.

This is my question. Why should the form necessarily be the same in all representations? To say that all diagonal elements (in any representation) are equal means that the probabilities for measuring all eigenvalues of any operator is the same. We may argue that the probability for measuring any energy eigenvalue within the specified range is the same (based on equal a priori probabilities).