Ivan Shishkin, Rye (1878)

Problems/Set theoryUnreviewed

Combien de boréliens ?

by La chouette aveugle·
70
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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On note Δ11(R)\mathbf{\Delta}_{1}^{1}(\mathbb{R}) l’ensemble des parties boréliennes de R\mathbb{R}. Montrer que ∣Δ11(R)∣=2ℵ0\lvert \mathbf{\Delta}_{1}^{1}(\mathbb{R})\rvert = 2^{\aleph_{0}}. En déduire qu’il existe des parties non boréliennes de R\mathbb{R}.

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