Oscillation of the Measure of Irrationality Function in the Multidimensional Case

It is proved that, for almost all pairs of $n\times m$ matrices $\Theta$, $\Theta'$, in the cases $m=1$ and $n=2$ or $m\ge2$ and $n=1$, the difference between the measure of irrationality functions $\psi_\Theta-\psi_{\Theta'}$ oscillates an infinite number of times as $t\to+\infty$.