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Chintschin has reported an exact proof of the most important theorems on the transmission of discrete information by noisy channels. This article deals with considerations leading to Shannon's first theorem; Chintschin's results are applied to quasi-periodic (hence, perforce, periodic) sources and channels. The crucial idea is that each quasi-periodic probability distribution is totally continuous with respect to its stationary mean value; McMillan's theorem is true for this; and, if McMillan's theorem is true for a distribution, it is also true for any distribution which is totally continuous with respect to it. Corresponding facts apply to quasi-periodic channels, so the whole theory can be reduced to the stationary case. Presumably, some existence problems associated with the transmission of signals form articifical earth satellites to fixed terrestrial stations are solved by this approach. (ERA citation 03:051549)