On LAO Testing of Multiple Hypotheses for Many Independent Objects
  The problem of many hypotheses logarithmically asymptotically optimal (LAO) testing for a model consisting of three or more independent objects is solved. It is supposed that $M$ probability distributions are known and each object independently of others follows to one of them. The matrix of asymptotic interdependencies (reliability--reliability functions) of all possible pairs of the error probability exponents (reliabilities) in optimal testing for this model is studied.   This problem was introduced (and solved for the case of two objects and two given probability distributions) by Ahlswede and Haroutunian. The model with two independent objects with $M$ hypotheses was explored by Haroutunian and Hakobyan. 
Evgueni A. Haroutunian (Associate Member, IEEE) and Parandzem M.   Hakobyan