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On the σ-class generated by open balls

Published online by Cambridge University Press:  01 July 1999

STEVE JACKSON  and
R. DANIEL MAULDIN
STEVE JACKSON
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-5116 e-mail: [email protected], e-mail: [email protected]
R. DANIEL MAULDIN
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-5116 e-mail: [email protected], e-mail: [email protected]
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Abstract

We show that in the finite dimensional space ℝd provided with a metric induced by a norm, the collection of Borel sets is the smallest collection containing the open balls and closed under complements and countable disjoint unions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 1 , July 1999 , pp. 99 - 108
Copyright
The Cambridge Philosophical Society 1999

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