Theorems · Theorem · functional analysis
MeasureTheory.MemLp.ofReal
∀ {α : Type u_1} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} {K : Type u_8} [inst : RCLike K]
{f : α → ℝ}, MeasureTheory.MemLp f p μ → MeasureTheory.MemLp (fun x => ↑(f x)) p μ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 231 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.
Cites9
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
- ENNRealstatement and proof · cited by 9,879
- RCLikestatement and proof · cited by 2,829
- MeasureTheory.MemLpstatement and proof · cited by 457
- RCLike.ofRealstatement · cited by 350
- RCLike.ofRealCLMproof · cited by 10
- ContinuousLinearMap.comp_memLp'proof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Integrable.ofRealproof · cited by 3
- MeasureTheory.memLp_re_im_iffproof · cited by 2
- TemperedDistribution.MemSobolev.fourier_memL1proof · cited by 0