Theorems · Theorem · measure theory
MeasureTheory.integral_const_mul
∀ {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), r * f a ∂μ = r * ∫ (a : α), f a ∂μ- Cited by
- 45 results in Mathlib
- Foundations
- Depth 253 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.
Cites6
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
- MeasureTheory.integralstatement · cited by 1,779
- MeasureTheory.integral_smulproof · cited by 23
Cited by45
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_mul_constproof · cited by 19
- Real.Gamma_one_half_eqproof · cited by 6
- indicator_indepFun_pi_of_prod_bcfproof · cited by 4
- ProbabilityTheory.covariance_smul_leftproof · cited by 4
- ProbabilityTheory.complexMGF_id_gaussianRealproof · cited by 3
- MeasureTheory.ext_of_integral_char_eqproof · cited by 3
- MeasureTheory.charFun_convproof · cited by 2
- ProbabilityTheory.lintegral_gammaPDF_eq_oneproof · cited by 2
- ProbabilityTheory.lintegral_gaussianPDFReal_eq_oneproof · cited by 2
- ProbabilityTheory.integral_cauchyPDFReal_eq_oneproof · cited by 2
- Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureTproof · cited by 2
- ProbabilityTheory.covariance_eq_subproof · cited by 2