Theorems · Theorem · real analysis
ContinuousMultilinearMap.contDiff
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {ι : Type u_2} {E : ι → Type u_3} [inst_3 : (i : ι) → NormedAddCommGroup (E i)]
[inst_4 : (i : ι) → NormedSpace 𝕜 (E i)] [inst_5 : Fintype ι] (f : ContinuousMultilinearMap 𝕜 E F) {n : WithTop ℕ∞},
ContDiff 𝕜 n ⇑f- Cited by
- 3 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Fintypestatement and proof · cited by 7,736
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- ContDiffstatement · cited by 352
- contDiff_iff_contDiffAtproof · cited by 28
- ContinuousMultilinearMap.contDiffAtproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- VectorFourier.norm_iteratedFDeriv_fourierPowSMulRightproof · cited by 2
- ContDiff.fourierPowSMulRightproof · cited by 1
- ContinuousMultilinearMap.iteratedFDeriv_comp_diagonalproof · cited by 0