Real Analysis Exchange

Box Dimension of the Limit of Hölder Functions

Loredana Biacino

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In this note a theorem to determine the box dimension of the graph of the limit of a sequence of α-Hölder functions is established. By application of such a theorem the box dimensions of the graphs of some functions that are generalizations of Weierstrass-type functions are determined.

Article information

Real Anal. Exchange, Volume 37, Number 1 (2011), 117-128.

First available in Project Euclid: 30 April 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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} 26A16: Lipschitz (Hölder) classes
Secondary: 26A30: Singular functions, Cantor functions, functions with other special properties

Hölder continuous functions box dimension Weierstrass-type functions


Biacino, Loredana. Box Dimension of the Limit of Hölder Functions. Real Anal. Exchange 37 (2011), no. 1, 117--128.

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