Theorems · Theorem · measure theory
NNRealRMK.lintegral_rieszMeasure
∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : T2Space X] [inst_2 : LocallyCompactSpace X]
[inst_3 : MeasurableSpace X] [inst_4 : BorelSpace X] (Λ : CompactlySupportedContinuousMap X NNReal →ₗ[NNReal] NNReal)
(f : CompactlySupportedContinuousMap X NNReal), ∫⁻ (x : X), ↑(f x) ∂NNRealRMK.rieszMeasure Λ = ↑(Λ f)The Riesz-Markov-Kakutani representation theorem: given a positive linear functional Λ,
the (lower) Lebesgue integral of f with respect to the rieszMeasure associated to Λ is equal
to Λ f.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- Realproof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- RingHom.idstatement and proof · cited by 18,349
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measureproof · cited by 10,939
- LinearMapstatement and proof · cited by 10,215
- ENNRealstatement and proof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- MeasureTheory.integralproof · cited by 1,779
- BorelSpacestatement and proof · cited by 1,602
- MeasureTheory.Integrableproof · cited by 1,367
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.