The asymptotic distribution function of the 4-dimensional shifted van der corput sequence

Let γ_q(n) be the van der Corput sequence in the base q and g(x, y, z, u) be an asymptotic distribution function of the 4-dimensional sequence

In this paper we find an explicit formula for g(x, x, x, x) and then as an example we find the limit

for the base q = 4, 5, 6, . . . Also we find an explicit form of sth iteration T^(s)(x) of the von Neumann-Kakutani transformation defined by T(γ_q(n)) = γ_q(n + 1).