Volver a Working Papers

Paper #226

Título:
A new light on Minkowski's? $(x)$ function
Autores:
Pelegrí Viader, Jaume Paradís y Lluís Bibiloni
Data:
Junio 1997
Resumen:
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.
Palabras clave:
Asymptotic distribution functions, Minkowski's function, singular functions
Códigos JEL:
C00
Área de investigación:
Estadística, Econometría y Métodos Cuantitativos
Publicado en:
Journal of Number Theory, 73, (1998), pp. 212-227

Descargar el paper en formato PDF