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Proceedings of the American Mathematical Society

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Borel measurability in linear algebra

Author: Edward A. Azoff
Journal: Proc. Amer. Math. Soc. 42 (1974), 346-350
MSC: Primary 15A60; Secondary 47C05
MathSciNet review: 0327799
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Abstract: It is shown that the usual processes of linear algebra (e.g., finding Jordan forms, eigenvalues, and eigenvectors) can be carried out in a Borel measurable fashion. These results follow easily from a variant of von Neumann's principle of measurable choice and can be applied to the study of Type $ {{\text{I}}_n}$ von Neumann algebras.

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Keywords: Borel function, linear algebraic process, principle of measurable choice, continuous matrix valued function on a Stonian space
Article copyright: © Copyright 1974 American Mathematical Society

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