Spectrum invariancy under output approximation full-rank discrete memoryless channels

The resolution of the process at the input of a given channel is the minimal undefinability of such processes at an output. Output statistics for these processes approximate the output statistics for the initial process as accurately as is wished. The formula for resolution of any process at the full-rank discrete memoryless channel input. The theorem is proved that if two processes at the input induce roughly the same output statistics than their corresponding information spectra (distributions of the normalized information densities) are nearly identical. The corollary of this theorem gives the following result: if the process at the input is steady and ergodic then its resolution coincides with its information velocity.