Theorems · Theorem · measure theory
MeasureTheory.MemLp.re
∀ {α : Type u_1} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} {𝕜 : Type u_5} [inst : RCLike 𝕜]
{f : α → 𝕜}, MeasureTheory.MemLp f p μ → MeasureTheory.MemLp (fun x => RCLike.re (f x)) p μ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 209 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.
Cites17
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
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Norm.normproof · cited by 5,413
- AddMonoidHomstatement · cited by 3,230
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- Filter.Eventually.of_forallproof · cited by 526
- MeasureTheory.MemLpstatement and proof · cited by 457
- AddMonoid.toZerostatement · cited by 325
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.memLp_re_im_iffproof · cited by 2
- MeasureTheory.Integrable.reproof · cited by 1