Theorems · Theorem · functional analysis
SchwartzMap.memLp
∀ {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F]
[inst_3 : NormedSpace ℝ F] [inst_4 : MeasurableSpace E] [OpensMeasurableSpace E] [SecondCountableTopologyEither E F]
(f : SchwartzMap E F) (p : ENNReal) (μ : autoParam (MeasureTheory.Measure E) SchwartzMap.memLp._auto_1)
[hμ : μ.HasTemperateGrowth], MeasureTheory.MemLp (⇑f) p μSchwartz functions are in L^p for any p.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- OpensMeasurableSpacestatement and proof · cited by 636
- MeasureTheory.MemLpstatement · cited by 457
- SchwartzMapstatement and proof · cited by 251
- SecondCountableTopologyEitherstatement and proof · cited by 117
- Continuous.aestronglyMeasurableproof · cited by 70
Cited by4
Results whose statement or proof uses this declaration.
- SchwartzMap.toLpproof · cited by 23
- SchwartzMap.coeFn_toLpproof · cited by 5
- SchwartzMap.norm_toLp'proof · cited by 1
- SchwartzMap.injective_toLpproof · cited by 0