Add to ORKGWe use entropy rates and Schur concavity to prove that, for every integer k ≥ 2, every nonzero rational number q, and every real number α, the base-k expansions of α, q+α, and qα all have the same finite-state dimension and the same finite-state strong dimension. This extends, and gives a new proof of, Wall’s 1949 theorem stating that the sum or product of a nonzero rational number and a Borel normal number is always Borel normal.
A new method for representing positive integers and real numbers in a rational base is considered. I...
This thesis studies some links between the combinatorial properties of the base-b expansion or of th...
We show that the set of absolutely normal numbers is Π03-complete in the Borel hierarchy of subsets ...
We use entropy rates and Schur concavity to prove that, for every integer k ≥ 2, every nonzero ratio...
AbstractWe use entropy rates and Schur concavity to prove that, for every integer k⩾2, every nonzero...
Classical Hausdorff dimension (sometimes called fractal dimension) was recently effectivized using g...
International audienceIn this paper we provide two equivalent characterizations of the notion of fin...
We give an elementary and direct proof of the following theorem: A real number is normal to a given ...
Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little i...
The base-k Copeland-Erdös sequence given by an infinite set A of positive integers is the infinite ...
The base-k Copeland-Erdős sequence given by an infinite set A of positive integers is the infinite s...
AbstractThe base-k Copeland–Erdös sequence given by an infinite set A of positive integers is the in...
Let s be an integer greater than or equal to 2. A real number is simply normal to base s if in its b...
AbstractThe set L of essentially non-normal numbers of the unit interval (i.e., the set of real numb...
The base-k Copeland-Erdös sequence given by an infinite set A of positive integers is the infinite ...
A new method for representing positive integers and real numbers in a rational base is considered. I...
This thesis studies some links between the combinatorial properties of the base-b expansion or of th...
We show that the set of absolutely normal numbers is Π03-complete in the Borel hierarchy of subsets ...
We use entropy rates and Schur concavity to prove that, for every integer k ≥ 2, every nonzero ratio...
AbstractWe use entropy rates and Schur concavity to prove that, for every integer k⩾2, every nonzero...
Classical Hausdorff dimension (sometimes called fractal dimension) was recently effectivized using g...
International audienceIn this paper we provide two equivalent characterizations of the notion of fin...
We give an elementary and direct proof of the following theorem: A real number is normal to a given ...
Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little i...
The base-k Copeland-Erdös sequence given by an infinite set A of positive integers is the infinite ...
The base-k Copeland-Erdős sequence given by an infinite set A of positive integers is the infinite s...
AbstractThe base-k Copeland–Erdös sequence given by an infinite set A of positive integers is the in...
Let s be an integer greater than or equal to 2. A real number is simply normal to base s if in its b...
AbstractThe set L of essentially non-normal numbers of the unit interval (i.e., the set of real numb...
The base-k Copeland-Erdös sequence given by an infinite set A of positive integers is the infinite ...
A new method for representing positive integers and real numbers in a rational base is considered. I...
This thesis studies some links between the combinatorial properties of the base-b expansion or of th...
We show that the set of absolutely normal numbers is Π03-complete in the Borel hierarchy of subsets ...