Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.ext_of_forall_lintegral_eq
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] [inst_1 : TopologicalSpace Ω] [HasOuterApproxClosed Ω] [BorelSpace Ω]
{μ ν : MeasureTheory.FiniteMeasure Ω},
(∀ (f : BoundedContinuousFunction Ω NNReal), ∫⁻ (x : Ω), ↑(f x) ∂↑μ = ∫⁻ (x : Ω), ↑(f x) ∂↑ν) → μ = νTwo finite Borel measures are equal if the integrals of all non-negative bounded continuous functions with respect to both agree.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- BorelSpacestatement and proof · cited by 1,602
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- BoundedContinuousFunctionstatement and proof · cited by 511
- MeasureTheory.FiniteMeasurestatement and proof · cited by 150
- MeasureTheory.FiniteMeasure.toMeasurestatement and proof · cited by 87
- HasOuterApproxClosedstatement and proof · cited by 65
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.FiniteMeasure.injective_toWeakDualBCNNproof · cited by 1
- MeasureTheory.FiniteMeasure.ext_of_forall_integral_eqproof · cited by 0