In the generalized paper, materials of physic-mathematical theory of hyper-random phenomenaoriented to description of statistically unstable physical phenomena are presented. Cognition questions of theworld are discussed from position of this theory. Different measurement models are researched. The hypothesisof statistical unpredictability and the hypothesis of hyper-random setting up of the world are analyzed. From thesehypotheses follow that cognition horizon is restricted by boundaries of unpredictable changes of researchedphysical phenomenon and of statistical conditions of their observations.
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