A new light on Minkowski's? $(x)$ function
| Autor: | Pelegrí Viader, Lluís Bibiloni, Jaume Paradís |
|---|---|
| Rok vydání: | 1997 |
| Předmět: |
Discrete mathematics
Pure mathematics Rational number Algebra and Number Theory Function (mathematics) jel:C00 Measure (mathematics) Null set Singularity Asymptotic distribution functions Minkowski's function singular functions Minkowski space Minkowski's question mark function Mathematics Real number |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|