Real Analysis Exchange

An Earlier Fractal Graph

Harvey Rosen

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Abstract

A function \(f:\mathbb{R}\to \mathbb{R}\) is additive if \( f(x+y)=f(x)+f(y)\) for all real numbers \(x\) and \(y\). We give examples of an additive function whose graph is fractal.

Article information

Source
Real Anal. Exchange, Volume 43, Number 2 (2018), 451-454.

Dates
First available in Project Euclid: 27 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.rae/1530064973

Digital Object Identifier
doi:10.14321/realanalexch.43.2.0451

Mathematical Reviews number (MathSciNet)
MR1922661

Zentralblatt MATH identifier
06924901

Subjects
Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 28A78: Hausdorff and packing measures 28A80: Fractals [See also 37Fxx]

Keywords
additive real function fractal graph

Citation

Rosen, Harvey. An Earlier Fractal Graph. Real Anal. Exchange 43 (2018), no. 2, 451--454. doi:10.14321/realanalexch.43.2.0451. https://projecteuclid.org/euclid.rae/1530064973


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