symmDiff — Mathlib

English

If S1 and S2 are measurable subsets of α, then their symmetric difference S1 Δ S2 is measurable.

Русский

Если A и B — измеримые подмножества α, то их симметрическая разность A Δ B измерима.

LaTeX

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

Lean4

@[simp, measurability]
protected theorem symmDiff {s₁ s₂ : Set α} (h₁ : MeasurableSet s₁) (h₂ : MeasurableSet s₂) : MeasurableSet (s₁ ∆ s₂) :=
  (h₁.diff h₂).union (h₂.diff h₁)

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