Vol. 28, No. 1, 1969

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A note on proposition observables

Stanley P. Gudder

Vol. 28 (1969), No. 1, 101–104

We consider some questions which were brought up in a previous paper: (1) If the product of two proposition observables is a proposition observable, do the corresponding propositions split? (2) What is the relationship, if any, between the concepts of compatibility and simultaneity of proposition observables? It is shown that the answer to (1) is yes and as a corollary we find the partial answer to (2) that compatibility implies simultaneity. It is also proved that the sum of two proposition observables is a proposition observable if and only if the corresponding propositions are orthogonal and also that (xa xb)n converges weakly to xab as n →∞.

Mathematical Subject Classification
Primary: 81.06
Received: 9 August 1967
Published: 1 January 1969
Stanley P. Gudder