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Zbl 0546.60019
Dunau, Jean-Louis; Sénateur, Henri
Quelles fonctions changent toute loi uniforme en une loi uniforme? (French)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 20, 247-250 (1984). ISSN 0246-0203

Consider a measurable function f:${\bbfR}\to {\bbfR}$ such that for any interval [a,b], if the random variable X is uniformly distributed on [a,b], then f(X) is uniformly distributed on some interval $[a\sb 1,b\sb 1]$ (depending on [a,b]). This paper proves that there exist 2 real numbers $\alpha$ and $\beta$ such that $f(x)=\alpha x+\beta$ for almost all x. This result has been stated without proof by {\it J. Pradines} and the reviewer in their paper in C. R. Acad. Sci., Paris, Ser. A 286, 399- 402 (1978; Zbl 0372.60012). The result is more delicate than it seems and the proof presented here is short and elegant.
[G.Letac]

MSC 2000:: *60E05 General theory of probability distributions
62E10 Structure theory of statistical distributions

Keywords: uniformly distributed

Citations: Zbl 0372.60012

Cited in: Zbl 1064.62060

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