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Observables in fuzzy probability theory

Gudder S.

Demonstratio Mathematica

1998

Vol. 31, nr 3

573-586

Properties of observables in a recently formulated fuzzy probability theory are investigated. After a review of definitions and terminology, we compare observables to probability kernels (or Markov kernels) and statistical maps which have been studied previously. We then discuss the spectrum of an observable and a spectral mapping theorem is proved. Finally, a special type of observable called an apparatus is introduced and its properties are studied.