Abstract
This paper states two equivalent conditions from which modularity of the latticeG of decision effectsE can be derived. It may be seen as a supplement to Ludwig's approach [5] to an axiomatic foundation of physical theories. As a consequence of these conditions every filterT E is a self-adjoint projector on the Hilber spaceB′ generated by the decision effects.
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This paper extends a final report presented to and supported by the Deutsche Forschungsgemeinschaft.
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Dähn, G. Symmetry of the physical probability function implies modularity of the lattice of decision effects. Commun.Math. Phys. 28, 123–132 (1972). https://doi.org/10.1007/BF01645511
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DOI: https://doi.org/10.1007/BF01645511