Geodesic
Singular Strictly Monotone Functions
Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 439-451.

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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. 
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A. A. Ryabinin; V. D. Bystritskii; V. A. Il'ichev. Singular Strictly Monotone Functions. Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 439-451. http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a12/

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