منابع مشابه
Normal Numbers from Steinhaus’ Viewpoint
Abstract. In this paper we recall a non-standard construction of the Borel sigma-algebraB in [0, 1] and construct a family of measures (in particular, Lebesgue measure) in B by a completely non-topological method. This approach, that goes back to Steinhaus, in 1923, is now used to introduce natural generalizations of the concept of normal numbers and explore their intrinsic probabilistic proper...
متن کاملNormal Numbers Are Normal
A number is normal in base b if every sequence of k symbols in the letters 0, 1, . . . , b− 1 occurs in the base-b expansion of the given number with the expected frequency b−k. From an informal point of view, we can think of numbers normal in base 2 as those produced by flipping a fair coin, recording 1 for heads and 0 for tails. Normal numbers are those which are normal in every base. In this...
متن کاملThe Three Gap Theorem (Steinhauss Conjecture)
We deal with the distribution of N points placed consecutively around the circle by a fixed angle of α. From the proof of Tony van Ravenstein [RAV88], we propose a detailed proof of the Steinhaus conjecture whose result is the following: the N points partition the circle into gaps of at most three different lengths. We study the mathematical notions required for the proof of this theorem reveal...
متن کاملPoly-Cauchy Numbers and Polynomials with Umbral Calculus Viewpoint
In this paper, we give some interesting identities of poly-Cauchy numbers and polynomials arising from umbral calculus.
متن کاملNormal numbers and finite automata
We give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the automata input-output behaviour is injective; they are also known as injective finite-state transdu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2012
ISSN: 0035-7596
DOI: 10.1216/rmj-2012-42-6-1953