Paper #226
- Títol:
- A new light on Minkowski's? $(x)$ function
- Autors:
- Pelegrà Viader, Jaume ParadÃs i LluÃs Bibiloni
- Data:
- Juny 1997
- Resum:
- 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.
- Paraules clau:
- Asymptotic distribution functions, Minkowski's function, singular functions
- Codis JEL:
- C00
- Àrea de Recerca:
- Estadística, Econometria i Mètodes Quantitatius
- Publicat a:
- Journal of Number Theory, 73, (1998), pp. 212-227
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