10 CL ´ EMENT DOMBRY, MICHAEL FALK, MAXIMILIAN ZOTT given by Hence, by (8), the attendant D -norm is for such x Note that ‖·‖$_{α}$ is defined as in (9), even though it does not define a norm in the case α < 1. Example 2.7 (Bernoulli model) . A simple example of a discrete generator is in- duced by independent Bernoulli- β random variables ˜ Z$_{i}$ , i = 1 , . . . , d , β ∈ (0 , 1], and putting Z$_{i}$ := ˜ Z$_{i}$/β , i = 1 , . . . , d . The D -norm and the dual D -norm function are easily derived. We have Note that ‖·‖$_{B}$$_{1}$ = ‖·‖$_{∞}$ and ‖·‖$_{B}$$_{β}$ → ‖·‖$_{1}$ as β → 0. Analogously, The aim of this section is to investigate the limit behaviour of the sample concur- rence probability. In Dombry et al. (2015), it is shown that the sample concurrence probability p$_{n}$ ( X ) of a rv X converges, provided that X has continuous margins and lies in the max-domain of attraction of a max-stable rv. We generalize this assertion to the functional setup, having in mind that we can formulate every result in the multivariate context analogously. Theorem 3.1. Let U $^{(1)}$, U $^{(2)}$, . . . be independent copies of a copula process U , satisfying U ∈ D ( η ) , where η is an SMSP with corresponding D -norm ‖·‖$_{D}$ . Then p$_{n}$ ( U ) = n ¯ π$_{n}$ ( U ) →$_{n}$$_{→∞}$ E ( ≀≀ η ≀≀$_{D}$ ) , 3. The functional extremal concurrence probability ≀≀ x ≀≀$_{B}$$_{β}$ = ∑ ̸ = T ⊂{ 1 ,...,d } β | T |− $^{1}$(1 − β ) d −| T | ≀≀ x$_{T}$ ≀≀$_{∞}$ , x ∈ R $^{d}$, β ∈ (0 , 1] . ‖ x ‖$_{B}$$_{β}$ = ∑ ̸ = T ⊂{ 1 ,...,d } β | T |− $^{1}$(1 − β ) d −| T | ‖ x$_{T}$ ‖$_{∞}$ , x ∈ R $^{d}$, β ∈ (0 , 1] . ‖ x ‖$_{W}$$_{α}$ = ∑ ̸ = T ⊂{ 1 ,...,d } ( − 1) | T |− $^{1}$( ‖ 1 / x$_{T}$ ‖$_{α}$ ) − $^{1}$, α > 0 . (10) ≀≀ x ≀≀$_{W}$$_{α}$ = ( ‖ 1 / x ‖$_{α}$ ) − $^{1}$, α > 0 .