IJPAM: Volume 52, No. 1 (2009)
Department of Algebra and Mathematical Analysis
University of Almería
Almería, 04120, SPAIN
Abstract.It is defined a representation system for numbers in the unit interval, generalising the dyadic one, and two dynamical systems are given which generate it. Metric results are especially derived from the second of them. The approximative coefficient is defined and studied with this second dynamical system. Moreover, it is deduced that, among other results, the Jager pair has the same distribution on a set of -measure 1, it is concentrated on a denumerable set of segments in and an explicit expression is given for it.
In addition, Gauss-Kuzmin-Levy and Limit Central Theorem type results are given for some random variables in connection with this representation numbers system.
Received: March 8, 2009
AMS Subject Classification: 26A30, 26A06, 26A09
Key Words and Phrases: dynamical system, dyadic representation system, measure preserving function, ergodicity, entropy, Jager pairs, Bernouillicity, identically distributed random variables
Source: International Journal of Pure and Applied Mathematics