Geodesic
On some questions related to the joint distribution of functionally dependent random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 3, pp. 541-548

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Consider the random vector $([sf_0(\eta)]_{m_0},\dots,[sf_N(\eta)]_{m_N})$ where $\eta$ is a random variable uniformly distributed on the interval $[0,2\pi]$; $s>0$ is a parameter and $[A]_m$ is the integral part of the least positive residue of a number $A$ modulo $m$. In the present paper, some classes of functions $f_0,\dots,f_N$ are found for which the distribution of this vector converges as $s\to\infty$ to the uniform distribution on integral points of $(N+1)$-dimensional rectangular $$ \{x\in R^{N+1}\quad0\le x_i,\quad i=0,l,\dots,N\}. $$ Estimates of convergence rates are given. 
@article{TVP_1971_16_3_a11,
     author = {Z. N. Saltykova},
     title = {On some questions related to the joint distribution of functionally dependent random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {541--548},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a11/}
}
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Z. N. Saltykova. On some questions related to the joint distribution of functionally dependent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 3, pp. 541-548. http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a11/