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Journal of the London Mathematical Society 1981 s2-23(3):534-536; doi:10.1112/jlms/s2-23.3.534
© 1981 by London Mathematical Society
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© Oxford University Press

Realcompactness and the Notion of Observable

Pavel Pták

Technical University of Prague, Faculty of Electrical Engineering, Department of Mathematics 166 27-Prague 6, Czechoslovakia

V. S. Varadarajan proved in [7] that any classical observable on the real line is a measurable mapping. We show in the present note that such a statement holds true for all realcompact spaces of nonmeasurable cardinality. This we think may find applications in the realm of quantum mechanics. Moreover, since realcompactness is always necessary our result may be viewed as a characterization of realcompact spaces (with the usual reservation for measurable cardinals).


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