A Typical Number is Extremely Non-Normal
نویسندگان
چکیده
Abstract Fix a positive integer N ? 2. For real number x ? [0, 1] and digit i {0, 1,..., ? 1}, let ? ( x, n ) denote the frequency of among first nN -adic digits . It is well-known that for typical (in sense Baire) 1], sequence frequencies diverges as ??. In this paper we show any regular linear transformation T there exists residual set points [0,1] such -averaged version (? )) also significantly.
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ژورنال
عنوان ژورنال: Uniform distribution theory
سال: 2022
ISSN: ['1336-913X', '2309-5377']
DOI: https://doi.org/10.2478/udt-2022-0001