Add to ORKGTHE aim of the present paper is to investigate the ergodic properties of the denominators dn in the Oppenheim expansion of real numbers into infinite series of rationals, which expansion includes, as special cases, Engel's, Sylvester's, and Liiroth's series and Cantor's infinite products. Thus our results generalize those obtained earlier for the latter expan-sions. I shall show that the sequence dn, considered on a specified probability space as random variables, forms a Markov chain, and that the sequence zn, a given function of dn and dn+1, of random variables is asymptotically uniformly distributed and the z's are 'almost indepen-dent ' (a term to be defined in the text) which facts suggest the validit...
Consider the infinite sequences of 0’s and 1’s, often called reals. Some of them are sufficiently “d...
In this course we give an introduction to the ergodic theory behind common number expansions, like e...
Following an axiomatic introduction to the prequential (predictive sequential) principle to statisti...
In this thesis we use modern developments in ergodic theory and uniform distribution theory to inves...
ABSTRACT. Generalized Zeckendorf decompositions are expansions of integers as sums of ele-ments of s...
The N-continued fraction expansion is a generalization of the regular continued fraction expansion, ...
The series is devoted to the publication of monographs and high-level textbooks in mathematics, math...
Abstract. We briefly present ongoing work about Martin-Löf randomness and the ergodic decompo-sitio...
A 2-continued fraction expansion is a generalisation of the regular continued fraction expansion, wh...
In this work we investigate the asymptotic behaviour of weighted partial sums of a particular class ...
Let ξ1,ξ2,. . . be a random sequence of r-ary digits, r ∈ N\{1}, connected into an ergodic Markov ch...
Graduation date: 1979By using continued fractions the set of positive\ud irrationals can be put in o...
Abstract. We investigate some properties connected with the alternating Lüroth-type se-ries represen...
This paper is concerned with probabilistic aspects of the expansion of points in n-dimensional Eucli...
In this thesis we research arithmetic progressions in random colourings of the integers. We ask ours...
Consider the infinite sequences of 0’s and 1’s, often called reals. Some of them are sufficiently “d...
In this course we give an introduction to the ergodic theory behind common number expansions, like e...
Following an axiomatic introduction to the prequential (predictive sequential) principle to statisti...
In this thesis we use modern developments in ergodic theory and uniform distribution theory to inves...
ABSTRACT. Generalized Zeckendorf decompositions are expansions of integers as sums of ele-ments of s...
The N-continued fraction expansion is a generalization of the regular continued fraction expansion, ...
The series is devoted to the publication of monographs and high-level textbooks in mathematics, math...
Abstract. We briefly present ongoing work about Martin-Löf randomness and the ergodic decompo-sitio...
A 2-continued fraction expansion is a generalisation of the regular continued fraction expansion, wh...
In this work we investigate the asymptotic behaviour of weighted partial sums of a particular class ...
Let ξ1,ξ2,. . . be a random sequence of r-ary digits, r ∈ N\{1}, connected into an ergodic Markov ch...
Graduation date: 1979By using continued fractions the set of positive\ud irrationals can be put in o...
Abstract. We investigate some properties connected with the alternating Lüroth-type se-ries represen...
This paper is concerned with probabilistic aspects of the expansion of points in n-dimensional Eucli...
In this thesis we research arithmetic progressions in random colourings of the integers. We ask ours...
Consider the infinite sequences of 0’s and 1’s, often called reals. Some of them are sufficiently “d...
In this course we give an introduction to the ergodic theory behind common number expansions, like e...
Following an axiomatic introduction to the prequential (predictive sequential) principle to statisti...