Theorems · Theorem · functional analysis
SchwartzMap.denseRange_toLpCLM
∀ {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] [inst_5 : OpensMeasurableSpace E]
[inst_6 : SecondCountableTopologyEither E F] [FiniteDimensional ℝ E] [BorelSpace E] {p : ENNReal},
p ≠ ⊤ →
∀ [hp' : Fact (1 ≤ p)] {μ : MeasureTheory.Measure E} [hμ : μ.HasTemperateGrowth]
[MeasureTheory.IsFiniteMeasureOnCompacts μ], DenseRange ⇑(SchwartzMap.toLpCLM ℝ F p μ)Schwartz functions are dense in Lp.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites50
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
- RingHom.idstatement · cited by 18,349
- 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
- Top.topstatement and proof · cited by 9,680
- ContinuousLinearMapstatement · cited by 5,352
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.fourier_toTemperedDistribution_eqproof · cited by 2
- SchwartzMap.toLp_fourier_eqproof · cited by 1
- SchwartzMap.toLp_fourierInv_eqproof · cited by 0