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It is well known that the Martin theory on positive harmonic functions plays an important role in the theory of open Riemann surfaces. Its whole theory depends upon the potential theory and the so-called Martin compactification of the given surface. In the present paper we shall give a proof of it, especially the representation theorem on positive harmonic functions on an end, which seems extremely simple. In our proof we shall introduce a suggestive functional and make use of a variationaldoi:10.2996/kmj/1138844322 fatcat:yg4wakkyf5e35iynjn3k64v3ja