Abstract
This paper studies a generalization of the a priori implication E<or=F, meaning of course EF=E, in the quantum logic P(H) of all projectors. The new definition can be applied also to new pairs of events, being based on the indistinguishability of some events when considered from the standpoint of a (fixed) state rho . The mathematical theory of factor Boolean algebras, on which this extension is based, is clarified.
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