Working Paper 226

Title:
A new light on Minkowski's? $(x)$ function
Authors:
Pelegrí Viader, Jaume Paradís and Lluís Bibiloni
Date:
June 1997
Abstract:
The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two ways: by exhibiting a set of measure one in which ?ï$(x)$ = 0; and again by actually finding a set of measure one which is mapped onto a set of measure zero and viceversa. These sets are described by means of metrical properties of different systems for real number representation.
Keywords:
Asymptotic distribution functions, Minkowski's function, singular functions
JEL codes:
C00
Area of Research:
Statistics, Econometrics and Quantitative Methods
Published in:
Journal of Number Theory, 73, (1998), pp. 212-227

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