Real Analysis Exchange

On I-Asymmetry

Mariusz Strześniewski

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Abstract

Sets of approximative asymmetry in the sense of category are introduced. The following theorem is proved. If $f : \mathbb{R}\to \mathbb{R}$ is a function, then the set of $\mathcal{I}$-asymmetry points of $f$ is of the type $F_{\sigma \delta \sigma}$ and is $\sigma$-well-porous. This illustrates the difference between measure and category. We give an example of a function with the set of $\mathcal{I}-$asymmetry points of the cardinality of the continuum.

Article information

Source
Real Anal. Exchange, Volume 26, Number 2 (2000), 593-602.

Dates
First available in Project Euclid: 27 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1214571352

Mathematical Reviews number (MathSciNet)
MR1844138

Zentralblatt MATH identifier
1031.26005

Subjects
Primary: 26A03: Foundations: limits and generalizations, elementary topology of the line 26E99: None of the above, but in this section

Keywords
cluster set $\cal I$-density porosity asymmetry set

Citation

Strześniewski, Mariusz. On I -Asymmetry. Real Anal. Exchange 26 (2000), no. 2, 593--602. https://projecteuclid.org/euclid.rae/1214571352


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