Theorems · Theorem · measure theory
MeasureTheory.Integrable.ofReal
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {𝕜 : Type u_8} [inst : RCLike 𝕜] {f : α → ℝ},
MeasureTheory.Integrable f μ → MeasureTheory.Integrable (fun x => ↑(f x)) μ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 232 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · 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.Integrablestatement and proof · cited by 1,367
- RCLike.ofRealstatement · cited by 350
- MeasureTheory.memLp_one_iff_integrableproof · cited by 73
- MeasureTheory.MemLp.ofRealproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_strongDualproof · cited by 3
- InformationTheory.integral_llr_compProd_eq_addproof · cited by 1
- integral_coe_re_add_coe_improof · cited by 1