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livre SVT bordas livre SVT seconde bordas dcg corrigé svt bacc 2012 énergie potentielle électostatique sepc devoires reacteurs chimiques devoires OCL EXERCICE Exercise 1.8.1 Proof the following assertion: The family of probability measures Pt1 ,...,tn on ( Rn, B( Rn)), n ≥ 1, t = (t1, .. . ,tn)> ∈ Tn fulfills the conditions of the theorem of Kolmogorov if and only if n ≥ 2 and for all s = (s1, .. . ,sn)> ∈ Rn the following conditions are fulfilled: a) ϕ Pt 1 ,...,tn ((s1, .. . ,sn)>) = ϕ Ptπ(1) ,...,tπ(n) ((sπ(1), .. . ,sπ(n))>) for all π ∈ Sn. b) ϕ Pt 1 ,...,tn−1 ((s1, .. . ,sn−1)>) = ϕ Pt1 ,...,tn ((s1, .. . ,sn−1, 0)>). Remark: ϕ(·) denotes the characteristic function of the corresponding measure. Sn denotes the group of all permutations π : {1, .. . ,n} → {1, .. . ,n}