Theorems · Theorem · measure theory

MeasureTheory.ext_of_forall_lintegral_eq_of_IsFiniteMeasure

∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] [inst_1 : TopologicalSpace Ω] [HasOuterApproxClosed Ω] [BorelSpace Ω]
  {μ ν : MeasureTheory.Measure Ω} [MeasureTheory.IsFiniteMeasure μ],
  (∀ (f : BoundedContinuousFunction Ω NNReal), ∫⁻ (x : Ω), ↑(f x) ∂μ = ∫⁻ (x : Ω), ↑(f x) ∂ν) → μ = ν

Two finite Borel measures are equal if the integrals of all non-negative bounded continuous functions with respect to both agree.

Defined in

Mathlib.MeasureTheory.Measure.HasOuterApproxClosed

Cited by

2 results in Mathlib

Foundations

Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceHasOuterApproxClosedBorelSpaceMeasureTheory.IsFiniteMeasure