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L3 A, int´egration : M363 – I – Exercices pr´eliminaires On pr´esente ici quelques m´ethodes de raisonnement qui seront utilis´ees en th´eorie de la mesure. Exercice 1 Pour tout entier naturel non nul n, on d´efinit les fonctions sym´etriques ´el´ementaires σn,k : Rn → R, l’entier k ´etant compris entre 0 et n, par : ∀α = (α1, · · · , αn) ∈ Rn, σn,k (α) = { 1 si k = 0 ∑ 1≤i1<···
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