  [**Proposition 0.0.**]{} [*Let $g\, :\, {I\!\!R}^k\to {I\!\!R}_+$ be a bounded borel function and assume that [**H0**]{}-[**H0**]{} hold. If $nh^k/(\log n)^{00\beta}\to\infty$ and $nh^{\alpha(k)} (\log n)^{0\beta}\to 0$, then for a.e. $t\in\Theta$ : $$\