Real Analysis Exchange

Hausdorff Dimension, Analytic Sets and Transcendence

G. A. Edgar and Chris Miller

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Every analytic real closed proper sub-field of $\mathbb R$ has Hausdorff dimension zero. Equivalently, every analytic set of real numbers having positive Hausdorff dimension contains a transcendence base for $\mathbb R$.

Article information

Real Anal. Exchange, Volume 27, Number 1 (2001), 335-340.

First available in Project Euclid: 6 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 28A78: Hausdorff and packing measures 03C64: Model theory of ordered structures; o-minimality 03E15: Descriptive set theory [See also 28A05, 54H05] 12L12: Model theory [See also 03C60]

Hausdorff dimension analytic sets Borel subrings real closed fields


Edgar, G. A.; Miller, Chris. Hausdorff Dimension, Analytic Sets and Transcendence. Real Anal. Exchange 27 (2001), no. 1, 335--340.

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