Before revision: After reviewing the strengthened hypotheses of the Shannon-MacMillan-Breiman Theorem, versus the standard statement of the Noiseless Coding Theorem, we state and prove a similar result for relative information , otherwise known as information gain. If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ).
After revision: This paper is part of an ongoing investigation of "pragmatic information", defined in Weinberger ( 2002 ).