Theorems · Theorem · functional analysis
WeakDual.seminormFamily_apply
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : SeminormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] (x : E) (f : WeakDual 𝕜 E), (WeakDual.seminormFamily 𝕜 E x) f = ‖f x‖- Defined in
- Mathlib.Analysis.Normed.Module.WeakDual
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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 · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Seminormstatement · cited by 272
- WeakDualstatement and proof · cited by 103
- WeakDual.seminormFamilystatement · cited by 3
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