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Mat. Zametki, 2004, Volume 76, Issue 3, Pages 439–451 (Mi mz120)  

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.

DOI: https://doi.org/10.4213/mzm120

Full text: PDF file (236 kB)
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English version:
Mathematical Notes, 2004, 76:3, 407–419

Bibliographic databases:

UDC: 517.5
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

Citation in format AMSBIB
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\paper Singular Strictly Monotone Functions
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\vol 76
\issue 3
\pages 439--451
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\jour Math. Notes
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. S. Kats, “Singular Strictly Increasing Functions and a Problem on Partitions of Closed Intervals”, Math. Notes, 81:3 (2007), 302–307  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Ramazanov A.-R.K., Magomedova V.G., Ibragimova B.M., “Otsenki modulei nepreryvnosti pervogo i vtorogo poryadkov dlya singulyarnykh funktsii”, Vestnik Dagestanskogo gosudarstvennogo universiteta, 2011, no. 1, 39–45  elib
  • Математические заметки Mathematical Notes
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