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Statistical maps. I: Basic properties. (English) Zbl 1088.81021
The author discusses recent results concerning statistical maps [E. Beltrametti and S. Bugajski, J. Math. Phys. 38, 3020–3030 (1997; Zbl 0874.06009); S. Bugajski, Intern. J. Theor. Phys. 35, 2229–2244 (1996; Zbl 0872.60003); S. Bugajski, K.-E. Hellwig and W. Stulpe, Rep. Math. Phys. 41, 1–11 (1998; Zbl 1026.60501)]. A statistical map is defined to be an affine map between two simplexes of probability measures satisfying a measurability condition. The author describes the closely related concepts of Markov kernels, dual statistical maps, statistical functions and effect-valued measures. He proves that a family of statistical maps possesses a natural product that is a statistical map.
Part II, cf. Math. Slovaca 51, No. 3, 343–361 (2001; Zbl 1088.81022).

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
60A99 Foundations of probability theory
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