Abstract
With the use of a suitable assumption about the structure of the class of experimental filters, it is shown that the sequence of alternating replicas of two filters is their greatest lower bound, as Jauch suggests. A generalization of his suggestion yields the greatest lower bound of a denumerable set of filters. The criteria of admissibility of filters are briefly discussed.
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References
Josef M. Jauch,Foundations of Quantum Mechanics (Addison-Wessley, Reading, Massachusetts, 1968).
Howard Stein, On the conceptual structure of quantum mechanics,Pittsburgh Series on Philosophy of Science, Vol. V, to be published.
R. Mirman, Analysis of the experimental meaning of coherent superposition and the nonexistence of superselection rules,Phys. Rev. D1, 3349 (1970), and references given there.
F. Riesz and B. Sz.-Nagy,Functional Analysis (Ungar, New York, 1955), p. 263.
John von Neuman,Functional Operators, Vol. II (Princeton University Press, Princeton, 1950). p. 55.
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Shimony, A. Filters with infinitely many components. Found Phys 1, 325–328 (1971). https://doi.org/10.1007/BF00708582
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DOI: https://doi.org/10.1007/BF00708582