Real Analysis Exchange

The Dynkin System Generated by the Large Balls of ℝn

Tamás Keleti

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Abstract

We prove that in an at least three dimensional Euclidean space the Dynkin system generated by the family of all open balls with radii at least one (that is, the smallest collection containing the open balls with radii at least one and closed under complements and countable disjoint unions) does not contain all Borel sets. We also give a simple characterization of the sets of this Dynkin system.

Article information

Source
Real Anal. Exchange, Volume 24, Number 2 (1999), 859-866.

Dates
First available in Project Euclid: 28 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.rae/1285689161

Mathematical Reviews number (MathSciNet)
MR1704760

Zentralblatt MATH identifier
0970.28002

Subjects
Primary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]

Keywords
balls Borel sets countable disjoint union complement

Citation

Keleti, Tamás. The Dynkin System Generated by the Large Balls of ℝ n. Real Anal. Exchange 24 (1999), no. 2, 859--866. https://projecteuclid.org/euclid.rae/1285689161


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