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This model has been studied intensely in Falk et al. (2015). The functions g$_{1}$, . . . , g$_{d}$ are continuous and satisfy conditions (2) and (5), so they provide an interpolating generalized max-linear model on C [0 , 1]. 

Example 2.2 . Choose pairwise different points s$_{1}$, . . . , s$_{d}$ ∈ [0 , 1] k and an arbitrary norm ‖·‖ on R $^{k}$. Define 

In order to normalize, put 

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These functions g$_{i}$ are well-defined since the denominator never vanishes: Suppose there is t ∈ [0 , 1] k with ˜ g$_{1}$ ( t ) = · · · = ˜ g$_{d}$ ( t ) = 0. Then min$_{j}$$_{̸}$$_{=}$$_{i}$ ( ‖ t − s$_{j}$ ‖ ) = 0 for all i = 1 , . . . , d . Now fix i ∈ { 1 , . . . , d } . There is j ̸ = i with t = s$_{j}$ . But on the other hand, we have also min$_{k}$$_{̸}$$_{=}$$_{j}$ ( ‖ t − s$_{k}$ ‖ ) = 0 which implies that there is k ̸ = j with t = s$_{k}$ = s$_{j}$ which is a contradiction. 

The functions g$_{i}$ , i = 1 , . . . , d , are clearly functions in ¯ C $^{+}$( [0 , 1] k ) that also satisfy condition (2) and (5) as can be seen as follows. We have for t ∈ [0 , 1] k 

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