Theorems · Theorem · functional analysis
SchwartzMap.eLpNorm_lt_top
∀ {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] (f : SchwartzMap E F) (p : ENNReal)
(μ : autoParam (MeasureTheory.Measure E) SchwartzMap.eLpNorm_lt_top._auto_1) [hμ : μ.HasTemperateGrowth],
MeasureTheory.eLpNorm (⇑f) p μ < ⊤The L^p norm of a Schwartz function is finite.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- 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 · cited by 9,680
- NNRealproof · cited by 4,310
- ENNReal.ofNNRealproof · cited by 1,279
- ENNReal.ofRealproof · cited by 863
- OpensMeasurableSpacestatement and proof · cited by 636
Cited by1
Results whose statement or proof uses this declaration.
- SchwartzMap.memLpproof · cited by 3