Methods of the Theory of Possibilities
in the Problems of Optimal Estimation and Decision Making I

(Measures of Possibility and Necessity and Integration
with respect to Possibility and Necessity)

Yu. P. Pyt’ev

Moscow State University, Vorob’evy gory, Moscow, 119899 Russia

Abstract—It is planned to set forth in a series of papers the fundamentals of the mathematical theory of possi
bilities in the same manner as probability theory is described, including limit theorems, and to discuss methods
of optimal estimation and decision making. The first paper deals with the constructions of measures of possi
bility, necessity, and of the integral.

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