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This article is cited in 2 scientific papers (total in 2 papers)
Singular Strictly Monotone Functions
A. A. Ryabinin, V. D. Bystritskii, V. A. Il'ichev N. I. Lobachevski State University of Nizhni Novgorod
Abstract:
We describe a universal approach to constructing continuous strictly monotone increasing singular functions on the closed interval $[-1,1]$. The “generator” of the method is the series $\sum_{k=1}^\infty\pm2^{-k}$ with random permutation of signs, and the corresponding functions are generated as distribution functions of such series. As examples, we consider two stochastic methods of arranging signs: independent and Markov.
Received: 10.04.2001 Revised: 18.06.2003
Citation:
A. A. Ryabinin, V. D. Bystritskii, V. A. Il'ichev, “Singular Strictly Monotone Functions”, Mat. Zametki, 76:3 (2004), 439–451; Math. Notes, 76:3 (2004), 407–419
Linking options:
https://www.mathnet.ru/eng/mzm120https://doi.org/10.4213/mzm120 https://www.mathnet.ru/eng/mzm/v76/i3/p439
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