Theorems · Theorem · measure theory

MeasureTheory.Measure.measure_toMeasurable_inter_of_cover

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
  MeasurableSet s →
    ∀ {t : Set α} {v : ℕ → Set α},
      t ⊆ ⋃ n, v n → (∀ (n : ℕ), μ (t ∩ v n) ≠ ⊤) → μ (MeasureTheory.toMeasurable μ t ∩ s) = μ (t ∩ s)

If a set t is covered by a countable family of finite measure sets, then its measurable superset toMeasurable μ t (which has the same measure as t) satisfies, for any measurable set s, the equality μ (toMeasurable μ t ∩ s) = μ (t ∩ s).

Defined in

Mathlib.MeasureTheory.Measure.Typeclasses.SFinite

Cited by

1 results in Mathlib

Foundations

Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound