restrict_nonzero_iff — Mathlib

English

Same content as restrict_apply_measure in 144316: for measurable s, (μ.restrict A)(s) = μ(s ∩ A).

Русский

То же, что и в restrict_apply_measure в п.144316: для измеримого s, (μ.restrict A)(s) = μ(s ∩ A).

LaTeX

$$$\forall s\ (s \text{ measurable})\; (\mu.restrict A)(s) = \mu(s \cap A)$$$

Lean4

theorem restrict_nonzero_iff (μ : FiniteMeasure Ω) (A : Set Ω) : μ.restrict A ≠ 0 ↔ μ A ≠ 0 := by
  rw [← mass_nonzero_iff, restrict_mass]

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