Informativity in the Category of Linear Measurement Systems

We construct the category of linear stochastic measurement systems (MS) that reflects the known features of the corresponding measurements. Both composition and product in this category allow for possible dependence of measurements. Some basic concepts are considered, such as independence and similarity of measurement systems; decomposition of measurement systems into simpler components is examined. The concept of informativity occupies a central place in the paper and its role emerges in connection with the synthesis of optimal MS. Specifically, a more informative MS produces a better result than a less informative MS.