content_image/317472.jpg content_image/317473.jpg content_image/317474.jpg content_image/317478.jpg content_image/317476.jpg content_image/317477.jpg
<img src='content_image/317472.jpg'>

Since every D -norm is monotone, we have 

<img src='content_image/317473.jpg'>

and, thus, by Lemma 2.3 (ii) 

<img src='content_image/317474.jpg'>

Remark 2.7 . The upper bound E (∣ ∣ Z$_{t}$ − ˆ Z$_{t}$ ∣ ) in Lemma 2.6 gets small if the distance between t and its nearest neighbor s$_{j}$ , say, in the grid { s$_{1}$, . . . , s$_{d}$ } gets small, which can be seen as follows. The triangle inequality implies 

From the condition g$_{i}$ ( s$_{j}$ ) = δ$_{ij}$ we obtain the representation 

and, thus, 

<img src='content_image/317478.jpg'>

<img src='content_image/317476.jpg'>

<img src='content_image/317477.jpg'>

