Theorems · Theorem · functional analysis
SchwartzMap.memSobolev
∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F]
[inst_2 : InnerProductSpace ℝ E] [inst_3 : FiniteDimensional ℝ E] [inst_4 : MeasurableSpace E] [inst_5 : BorelSpace E]
[inst_6 : NormedSpace ℂ F] [inst_7 : CompleteSpace F] {s : ℝ} {p : ENNReal} [hp : Fact (1 ≤ p)] (f : SchwartzMap E F),
TemperedDistribution.MemSobolev s p ((SchwartzMap.toTemperedDistributionCLM E F MeasureTheory.volume) f)Schwartz functions are in every Sobolev space.
- Defined in
- Mathlib.Analysis.Distribution.Sobolev
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 308 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · 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
- ENNRealstatement and proof · cited by 9,879
- Set.Elemstatement · cited by 7,166
- Set.ofPredstatement · cited by 6,101
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
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