Add to ORKGLet m ≥ 2 be a natural number. Let νmλ be the distribution of the random sum ∞P n=0 θnλ n, where θn are i.i.d. and for every n the random variable θn takes value in the set {0,...,m−1} with equal probabilities. As a generalization of Solomyak Theorem we prove that for Lebesgue a.e. λ ∈ (1/m, 1) the measure νmλ is absolute continuous w.r.t. the Lebesgue measure. (For smaller λ, the measure νmλ is supported by a Cantor-set, so if λ < 1/m then νmλ is singular.)
In this thesis we use modern developments in ergodic theory and uniform distribution theory to inves...
Denote by $\mu_a$ the distribution of the random sum $(1-a) \sum_{j=0}^\infty \omega_j a^j$, where $...
For $1 \le p < \infty$, the Fr\'echet $p$-mean of a probability distribution $\mu$ on a metric space...
Construct a probability measure $\mu$ on the circle by successive removal of middle third intervals ...
Let S=(s_1<s_2<\dots) be a strictly increasing sequence of positive integers and denote e(b):=exp(2\...
Let S=(s_1<s_2<\dots) be a strictly increasing sequence of positive integers and denote e(b):=exp(2\...
Let S := (s_1 < s_2 < . . . ) be a strictly increasing sequence of positive integers and denote e(β)...
. We study the distributions F`;p of the random sums P 1 1 " n` n , where " 1 ; "...
Motivated by the random covering problem and the study of Dirichlet uniform approximable numbers, we...
In 1923 A. Khinchin asked if given any B ? [0, 1) of positive Lebesgue measure, we have #{n : 1 ≤ n ...
The first section of this chapter starts with the Buffon problem, which is one of the oldest in stoc...
AbstractIf (xn) is a monotone sequence of reals that is uniformly distributed mod 1, then it is show...
Since the 1930's many authors have studied the distribution of the random series Y = P n where ...
Abstract. Let X1,..., XN denote N independent d-dimensional Lévy processes, and con-sider the N-par...
Let ξ1,ξ2,. . . be a random sequence of r-ary digits, r ∈ N\{1}, connected into an ergodic Markov ch...
In this thesis we use modern developments in ergodic theory and uniform distribution theory to inves...
Denote by $\mu_a$ the distribution of the random sum $(1-a) \sum_{j=0}^\infty \omega_j a^j$, where $...
For $1 \le p < \infty$, the Fr\'echet $p$-mean of a probability distribution $\mu$ on a metric space...
Construct a probability measure $\mu$ on the circle by successive removal of middle third intervals ...
Let S=(s_1<s_2<\dots) be a strictly increasing sequence of positive integers and denote e(b):=exp(2\...
Let S=(s_1<s_2<\dots) be a strictly increasing sequence of positive integers and denote e(b):=exp(2\...
Let S := (s_1 < s_2 < . . . ) be a strictly increasing sequence of positive integers and denote e(β)...
. We study the distributions F`;p of the random sums P 1 1 " n` n , where " 1 ; "...
Motivated by the random covering problem and the study of Dirichlet uniform approximable numbers, we...
In 1923 A. Khinchin asked if given any B ? [0, 1) of positive Lebesgue measure, we have #{n : 1 ≤ n ...
The first section of this chapter starts with the Buffon problem, which is one of the oldest in stoc...
AbstractIf (xn) is a monotone sequence of reals that is uniformly distributed mod 1, then it is show...
Since the 1930's many authors have studied the distribution of the random series Y = P n where ...
Abstract. Let X1,..., XN denote N independent d-dimensional Lévy processes, and con-sider the N-par...
Let ξ1,ξ2,. . . be a random sequence of r-ary digits, r ∈ N\{1}, connected into an ergodic Markov ch...
In this thesis we use modern developments in ergodic theory and uniform distribution theory to inves...
Denote by $\mu_a$ the distribution of the random sum $(1-a) \sum_{j=0}^\infty \omega_j a^j$, where $...
For $1 \le p < \infty$, the Fr\'echet $p$-mean of a probability distribution $\mu$ on a metric space...