Linearity of expectation functionals

Foundations of Physics 15 (1):101-111 (1985)
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Abstract

LetB be the set of bounded observables on a quantum logic. A mapJ: B →R is called an expectation functional ifJ is normalized, positive, continuous, and compatibly linear. Two questions are considered. IsJ linear, and isJ an expectation relative to some state? It is shown that the answers are affirmative for hidden variable logics and most Hilbert space logics. An example is given which shows thatJ can be nonlinear on an arbitrary quantum logic

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Generalized measure theory.Stanley Gudder - 1973 - Foundations of Physics 3 (3):399-411.

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