2 MICHAEL FALK, MAXIMILIAN ZOTT MSE (IMSE) is established if the set of grid points s$_{1}$, . . . , s$_{d}$ gets dense in the index space. A max-stable random process with index set T is a family of random variables ξ = ( ξ$_{t}$ )$_{t}$$_{∈}$$_{T}$ with the property that there are functions a$_{n}$ : T → R + 0 and b$_{n}$ : T → R , n ∈ N , such that where ξ ( i ) = ( ξ ( i ) t )$_{t}$$_{∈}$$_{T}$ , i = 1 , . . . , n , are independent copies of ξ and ’=$_{d}$’ denotes equality in distribution. We get a max-stable random vector (rv) on R d by putting T = { 1 , . . . , d } . Different to that, we obtain a max-stable process with continuous sample paths on some compact metric space S , if we set T = S and require that the sample paths ξ ( ω ) : S → R realize in C ( S ) = { g ∈ R S : g continuous } , and that the norming functions a$_{n}$, b$_{n}$ are continuous as well. Max-stable random vectors, and processes, respectively, have been investigated intensely over the last decades. For detailed reviews of max-stable rv and processes, see for instance the monographies of Beirlant et al. (2004), de Haan and Ferreira (2006), Resnick (2008), Falk et al. (2011) and Davison et al. (2012 b ) among others. Max-stable rv and processes are of enormous interest in extreme value theory since they are the only possible limit of linearly standardized maxima of independent and identically distributed rv or processes. Clearly, the univariate margins of a max-stable random process are max-stable distributions on the real line. A max-stable random object ξ = ( ξ$_{t}$ )$_{t}$$_{∈}$$_{T}$ is commonly called simple max-stable in the literature if each univariate margin is unit Fr´ echet distributed, i. e. P ( ξ$_{t}$ ≤ x ) = exp ( − x − $^{1}$) , x > 0, t ∈ T . Different to that, we call a random process η = ( η$_{t}$ )$_{t}$$_{∈}$$_{T}$ standard max-stable if all univariate marginal distributions are standard negative exponential, i. e. P ( η$_{t}$ ≤ x ) = exp ( x ), x ≤ 0, t ∈ T . The transformation to simple/standard margins does not cause any problems, neither in the case of rv (see e. g. de Haan and Resnick (1977) or Resnick (2008)), nor in the case of rf with continuous sample paths (see e. g. Gin´ e et al. (1990)). ( max i =1 ,...,n ( ξ ( i ) t − b$_{n}$ ( t ) a$_{n}$ ( t ) ))$_{t}$$_{∈}$$_{T}$ =$_{d}$ ξ ,