content_image/298236.jpg content_image/298235.jpg content_image/298234.jpg
But elementary computations show that Δ b $_{a}$H$_{1}$ = 0, i.e., Q is the null measure on ( − ∞ , 0 ]. 

Instead one can define Q on [ −∞ , 0] $^{d}$\ {− ∞ } by putting for x$_{i}$ ≤ 0 and i = 1 , . . . , d 

<img src='content_image/298236.jpg'>

Then Q has its complete mass on the set { ⋃ i =1 ( {−∞} $^{1}$× ( −∞ , 0] ×{−∞} )} and 

<img src='content_image/298235.jpg'>

This approach is closely related to the formulation of the exponent measure theorem as in Balkema and Resnick (1977) and Vatan (1985). 

Take, on the other hand, ‖·‖$_{D}$ = ‖·‖$_{∞}$ , which is the least D -norm. In this case, the components η$_{1}$, . . . , η$_{d}$ of η are completely dependent, i.e., η$_{1}$ = η$_{2}$ = · · · = η$_{d}$ a.s. and, thus, 

which is a max-stable distribution (MSD). 

<img src='content_image/298234.jpg'>

