inter — Mathlib

English

If S1 and S2 are measurable subsets of α, then their intersection is measurable.

Русский

Если A и B — измеримые подмножества α, то их пересечение измеримо.

LaTeX

$$$\mathrm{MeasurableSet}(s_1) \rightarrow \mathrm{MeasurableSet}(s_2) \rightarrow \mathrm{MeasurableSet}(s_1 \cap s_2)$$$

Lean4

@[simp, measurability]
protected theorem inter {s₁ s₂ : Set α} (h₁ : MeasurableSet s₁) (h₂ : MeasurableSet s₂) : MeasurableSet (s₁ ∩ s₂) :=
  by
  rw [inter_eq_compl_compl_union_compl]
  exact (h₁.compl.union h₂.compl).compl

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