Theorems · Theorem · measure theory
MeasureTheory.integral_mul_const
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {L : Type u_6} [inst : RCLike L] (r : L)
(f : α → L), ∫ (a : α), f a * r ∂μ = (∫ (a : α), f a ∂μ) * r- Cited by
- 19 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- RCLikestatement and proof · cited by 2,829
- mul_commproof · cited by 2,262
- MeasureTheory.integralstatement and proof · cited by 1,779
- MeasureTheory.integral_const_mulproof · cited by 45
Cited by19
Results whose statement or proof uses this declaration.
- integral_cexp_quadraticproof · cited by 5
- MeasureTheory.charFun_convproof · cited by 2
- MeasureTheory.integral_divproof · cited by 2
- ProbabilityTheory.covariance_eq_subproof · cited by 2
- continuousOn_integral_bilinear_of_locally_integrable_of_compact_supportproof · cited by 2
- ProbabilityTheory.Kernel.HasSubgaussianMGF.add_compProdproof · cited by 1
- MeasureTheory.charFun_map_add_constproof · cited by 1
- ProbabilityTheory.iteratedDeriv_two_cgf_eq_integralproof · cited by 1
- integral_pow_mul_le_of_le_of_pow_mul_leproof · cited by 1
- MeasureTheory.dist_convolution_le'proof · cited by 1
- Complex.Gamma_mul_Gamma_eq_betaIntegralproof · cited by 1