E. Borel. Sur les probabilites denombrables et leurs applications arithmetiques. Rend. Circ. Mat. Palermo, 27:247--271, 1909. Home/Search Document Not in Database Summary Related Articles Check |
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Hyperbolicity And Recurrence In Dynamical Systems: A Survey Of.. - Barreira (2002) (1 citation) (Correct)
....of the dimensional properties. For each k # 0, m 1 , x [0, 1] and n # k (x, n) card i # 1, n : x i = k . Whenever there exists the limit # k (x) lim it is called the frequency of the number k in the base m representation of x. A classical result of Borel [25] says that for Lebesgue almost every x [0, 1] we have # k (x) 1 m for every k. Furthermore, for m = 2, Hardy and Littlewood [50] showed that for Lebesgue almost every x [0, 1] k = 0, 1, and all su#ciently large n, # # n # # log n n . In particular, Lebesgue almost all ....
E. Borel, Sur les probabilites denombrables et leurs applications arithmetiques, Rend. Circ. Mat. Palermo 26 (1909), 247--271.
Distribution of Frequencies of Digits Via Multifractal.. - Barreira, Saussol.. (1 citation) (Correct)
....k (x, n) card i . n : x i = k . Whenever there exists the limit # k (x) lim (1) it is called the frequency of the number k in the base m representation of x. When we write the symbol # k (x) we are already assuming the existence of the limit in (1) A classical result of Borel [6] says that for Lebesgue almost every x we have # k (x) 1 m for every k. Furthermore, for m = 2, Hardy and Littlewood [10] showed that for Lebesgue almost every x [0, 1] k = 0, 1, and all su#ciently large n, # # n # # log n n . 2000 Mathematics Subject Classification. ....
E. Borel, Sur les probabilites denombrables et leurs applications arithmetiques, Rend. Circ. Mat. Palermo 26 (1909), 247--271.
Dimensions of Copeland-Erdos Sequences - Xiaoyang Gu Jack (Correct)
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E. Borel. Sur les probabilites denombrables et leurs applications arithmetiques. Rend. Circ. Mat. Palermo, 27:247--271, 1909.
Dimensions of Copeland-Erdos Sequences - Gu, Lutz, Moser (2005) (Correct)
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E. Borel. Sur les probabilites denombrables et leurs applications arithmetiques. Rend. Circ. Mat. Palermo, 27:247--271, 1909.
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