Working Paper 226

A new light on Minkowski's? $(x)$ function
Pelegrí Viader, Jaume Paradís and Lluís Bibiloni
June 1997
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.
Asymptotic distribution functions, Minkowski's function, singular functions
JEL codes:
Area of Research:
Statistics, Econometrics and Quantitative Methods
Published in:
Journal of Number Theory, 73, (1998), pp. 212-227

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