Theorems · Theorem · measure theory
integral_conj
∀ {X : Type u_1} [inst : MeasurableSpace X] {μ : MeasureTheory.Measure X} {𝕜 : Type u_6} [inst_1 : RCLike 𝕜]
{f : X → 𝕜}, ∫ (x : X), (starRingEnd 𝕜) (f x) ∂μ = (starRingEnd 𝕜) (∫ (x : X), f x ∂μ)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpaceRCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- RingHomstatement · cited by 10,189
- RCLikestatement and proof · cited by 2,829
- MeasureTheory.integralstatement · cited by 1,779
- starRingEndstatement · cited by 671
- LinearIsometryEquiv.toLinearIsometryproof · cited by 39
- RCLike.conjLIEproof · cited by 4
- LinearIsometry.integral_comp_commproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Complex.GammaIntegral_conjproof · cited by 1