|
Title:
|
A New Light on Minkowski's? $(x)$ Function
|
|
Author:
|
Viader, Pelegrí; Paradís, Jaume; Bibiloni, Lluís
|
|
Other authors:
|
Universitat Pompeu Fabra. Departament d'Economia i Empresa |
|
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. |
|
Publication date:
|
2005-09-15 |
|
Subject(s):
|
Asymptotic distribution functions, Minkowski's function, singular functions |
|
Rights:
|
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el departament i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
|
Document type:
|
Working Paper |
|
Share:
|
|
