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Methods of reduction of measurements in Hilbert spaces. (English. Russian original) Zbl 0603.94006

Math. USSR, Sb. 54, 525-549 (1986); translation from Mat. Sb., Nov. Ser. 126(168), No. 4, 543-565 (1985).
The basic facts are given in the theory of random elements and random operators acting in Hilbert spaces. Reduction methods are developed for several models for a measurement scheme, including methods for a model with a random operator.

MSC:

94A34 Rate-distortion theory in information and communication theory
47A50 Equations and inequalities involving linear operators, with vector unknowns
60H25 Random operators and equations (aspects of stochastic analysis)
65C20 Probabilistic models, generic numerical methods in probability and statistics
94A15 Information theory (general)
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