Theorems · Theorem · measure theory

MeasureTheory.Measure.measure_inter_eq_of_measure_eq

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

If u is a superset of t with the same (finite) measure (both sets possibly non-measurable), then for any measurable set s one also has μ (t ∩ s) = μ (u ∩ s).

Defined in

Mathlib.MeasureTheory.Measure.MeasureSpace

Cited by

2 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound