Abstract vector spaces applied to problems in detection and estimation theory

The concepts of abstract vector spaces are summarized and applied to such problems as the detection of binary signals in additive Gaussian noise and the maximum a posteriori estimation of analog signals transmitted over random fading media. Although the results obtained are in most cases well known in the literature, it is felt that the abstract vector approach provides notational and manipulative simplicity that warrants its extension to other problems in detection and estimation theory.