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which is condition (2). Note, moreover, that ˜ g$_{i}$ ( s$_{j}$ ) = 0 if i ̸ = j . But this implies condition (5): 

by the fact that a D -norm of each unit vector in R d is one. Thus, we have found an interpolating generalized max-linear model on C ( [0 , 1] $^{k}$) . 

The mean squared error of the discretized version. We start this section with a result that applies to bivariate standard max-stable rv in general. 

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Lemma 2.3. Let ( X$_{1}$, X$_{2}$ ) be standard max-stable with generator ( Z$_{1}$, Z$_{2}$ ) and D - norm ‖·‖$_{D}$ . 

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Proof. (i) See Falk et al. (2015, Lemma 3.6). 

(ii) The assertion follows from the general identity max( a, b ) = 1 $_{2}$( a + b + | a − b | ). □ 

Let ˆ η = (ˆ η$_{t}$ )$_{t}$$_{∈}$$_{[0}$$_{,}$$_{1]}$ k be the discretized version of η = ( η$_{t}$ )$_{t}$$_{∈}$$_{[0}$$_{,}$$_{1]}$ k with grid { s$_{1}$, . . . , s$_{d}$ } and weight functions g$_{1}$, . . . , g$_{d}$ . In order to calculate the mean squared error of ˆ η$_{t}$ , we need the following lemma. 

Lemma 2.4. Let ˆ Z = ( ˆ Z$_{t}$ )$_{t}$$_{∈}$$_{[0}$$_{,}$$_{1]}$ k be the generator of ˆ η that is defined in (4) . For each t ∈ [0 , 1] $^{k}$, the rv ( η$_{t}$, ˆ η$_{t}$ ) is standard max-stable with generator ( Z$_{t}$, ˆ Z$_{t}$ ) and 

