Abstract
The paper is devoted to a game problem of approaching at a fixed terminal moment. Closed sets in the space of positions of the game are considered, which, generally speaking, do not satisfy the stability property. The notion of stability defect of these sets is studied. This notion was introduced by the authors earlier. A positional strategy of the first player extremal with respect to these sets on some of their chosen neighborhoods is shown to ensure at the terminal moment a deviation of the system's motions not larger than the stability defect of these sets.
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