Before revision:  Both the theorem proven herein and the application to trading make a compelling case for Weinberger's definition of pragmatic information .
After revision:  A second application is to the question of market efficiency. An efficient market is, by definition, a market in which the pragmatic information of the "tradable past" with respect to current prices is zero. Under this definition, markets whose returns are characterized by a GARCH(1,1) process cannot be efficient. Finally, a pragmatic informational analogue to Shannon's Noisy Coding Theorem suggests that a cause of market inefficiency is that the underlying fundamentals are changing so fast that the price discovery mechanism simply cannot keep up. This may happen most readily in the run-up to a financial bubble, where investors' willful ignorance degrade the information processing capabilities of the market .