Theorems · Theorem · measure theory

MeasureTheory.OuterMeasure.IsMetric.borel_le_caratheodory

∀ {X : Type u_2} [inst : EMetricSpace X] {μ : MeasureTheory.OuterMeasure X}, μ.IsMetric → borel X ≤ μ.caratheodory

Carathéodory's theorem. If m is a metric outer measure, then every Borel measurable set t is Carathéodory measurable: for any (not necessarily measurable) set s we have μ (s ∩ t) + μ (s \ t) = μ s.

Defined in

Mathlib.MeasureTheory.Measure.Hausdorff

Cited by

1 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

EMetricSpace