Theorems · Theorem · functional analysis

Distribution.TemperedDistribution.IsVanishingOn.smulLeftCLM

∀ {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E] [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace ℝ E]
  [inst_3 : NormedSpace ℂ F] {f : TemperedDistribution E F} {s : Set E},
  Distribution.IsVanishingOn (⇑f) s →
    ∀ {g : E → ℂ},
      Function.HasTemperateGrowth g → Distribution.IsVanishingOn (⇑((TemperedDistribution.smulLeftCLM F g) f)) s

Defined in: Mathlib.Analysis.Distribution.Support
Cited by: 2 results in Mathlib
Foundations: Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedAddCommGroup NormedSpace NormedSpace

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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
Setstatement and proof · cited by 53,352
Realstatement and proof · cited by 25,697
RingHom.idstatement · cited by 18,349
NormedAddCommGroupstatement and proof · cited by 15,752
NormedSpacestatement and proof · cited by 12,499
Set.Elemstatement · cited by 7,166
Set.ofPredstatement · cited by 6,101
Complexstatement and proof · cited by 5,565
ContinuousLinearMapstatement · cited by 5,352
LE.le.transproof · cited by 3,151
Finitestatement · cited by 3,029

Cited by2

Results whose statement or proof uses this declaration.

Distribution.TemperedDistribution.dsupport_smulLeftCLM_subsetproof · cited by 1
Distribution.IsVanishingOn.smulLeftCLMproof · cited by 0