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Measures on infinite-dimensional orthomodular spaces

  • Part I. Invited Papers Dedicated To The Memory Of Charles H. Randall (1928–1987)
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Abstract

We classify the measures on the lattice ℒ of all closed subspaces of infinite-dimensional orthomodular spaces (E, Ψ) over fields of generalized power series with coefficients in ℝ. We prove that every σ-additive measure on ℒ can be obtained by lifting measures from the residual spaces of (E, Ψ). The measures being lifted are known, for the residual spaces are Euclidean. From the classification we deduce, among other things, that the set of all measures on ℒ is not separating.

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  1. Institut für Mathematische Statistik, Universität Bern, Sidlerstrasse 5, CH-3000, Bern, Switzerland

    Hans A. Keller

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  1. Hans A. Keller
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Research supported by the Swiss National Science Foundation.

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Keller, H.A. Measures on infinite-dimensional orthomodular spaces. Found Phys 20, 575–604 (1990). https://doi.org/10.1007/BF01883240

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