# Article

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Keywords:
random $n$-ary sequences; uniform distribution
Summary:
Višek [3] and Culpin [1] investigated infinite binary sequence $X=(X_1,X_2,\dots )$ with $X_i$ taking values $0$ or $1$ at random. They investigated also real mappings $H(X)$ which have the uniform distribution on $[0;1]$ (notation $\mathcal U(0;1)$). The problem for $n$-ary sequences is dealt with in this paper.
References:
[1] D. Culpin: Distribution of random binary sequence. Aplikace matematiky 25 (1980), 408–416. MR 0596847
[2] I.I. Gichman, A.V. Skorochod: Introduction to the theory of random processes. Moskva, 1977.
[3] J.A. Višek: On properties of binary random numbers. Aplikace matematiky 19 (1974), 375–385. MR 0375442
[4] J. Hájek, Z. Šidák: Theory of rank tests. Prague, 1967. MR 0229351
[5] W. Feller: An introduction to probability theory and its applications. New York, 1971. Zbl 0219.60003
[6] D. Dacunha-Castelle, M. Duflo: Probalilités et statistiques. Paris, 1983.

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