5 ON FUNCTIONAL RECORDS AND CHAMPIONS Different to records, the concept of multivariate and functional champions is very recent. It has been established in the work of Dombry et al. (2015). In their paper, they derive the limit sample concurrence probability under iid rv X $^{(1)}$, . . ., X ( n ) in R $^{d}$. There are also many results on statistical inference in their work. In Section 3, we generalize the limit sample concurrence probability which has been derived in Dombry et al. (2015, Theorem 2) to the case of stochastic processes with continuous sample paths. Further, we compute the distribution of a champion, given that there actually is one. Section 4 deals with simple record times and the distribution of simple records, where all considerations are restricted to the finitedimensional case. To begin with, we introduce a mapping which is strongly related to the D - norm of an SMSP, and which will be important troughout the whole paper. Let ‖·‖$_{D}$ be a D -norm generated by Z = ( Z$_{s}$ )$_{s}$$_{∈}$$_{S}$ in ¯ C $^{+}$( S ), (recall E ( Z$_{s}$ ) = 1 and E (sup$_{s}$$_{∈}$$_{S}$ Z$_{s}$ ) < ∞ ). We call the mapping the dual D -norm function corresponding to ‖·‖$_{D}$ . Note that, despite the fact that the generator of ‖·‖$_{D}$ is not uniquely determined, the dual D -norm function ≀≀ · ≀≀$_{D}$ does not depend on the choice of the generator of ‖·‖$_{D}$ . This is a consequence of Aulbach et al. (2013, Lemma 6). Therefore, the mapping is well-defined, although not one-to-one, since different D -norms can lead to the same dual D -norm function. One can check that the dual D -norm function is always zero if there are at least two independent components η$_{s}$, η$_{t}$ of the SMSP η generated by ‖·‖$_{D}$ , since Takahashi’s theorem (Falk et al. (2011, Theorem 4.4.1)) ‖·‖$_{D}$ → ≀≀ · ≀≀$_{D}$ ≀≀ · ≀≀$_{D}$ : E ( S ) → R , f ↦→ ≀≀ f ≀≀$_{D}$ := E ( inf s ∈ $_{S}$| f ( s ) | Z$_{s}$ ) , 2. The dual D -norm function