Ivan Shishkin, Rye (1878)

Problems/Measure theoryExerciseUnreviewed

Mesurabilité de quelques applications.

by SalixBabylonica·
31
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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  1. Soit (E,T)(E,\mathcal T) un espace mesurable. Montrer que l’identité Id⁡E:E→E\operatorname{Id}_E:E\to E est mesurable.

  2. Soit (X,A)(X,\mathcal A) un espace mesurable et A∈AA \in \mathcal A.
    La fonction indicatrice de AA est-elle mesurable ?

  3. Soit (E1,T1), (E2,T2)(E_{1},\mathcal T_{1}),\, (E_{2}, \mathcal T_{2}) deux espaces mesurables. Soit f:E1↦E2f : E_{1} \mapsto E_{2} et g:E2↦E1g: E_{2} \mapsto E_{1}, deux applications mesurables.
    L’application f∘gf\circ g est-elle mesurable ?

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