Theorems · Theorem · functional analysis
lp.ext_continuousAddMonoidHom_iff
∀ {α : Type u_3} {E : α → Type u_4} {p : ENNReal} [inst : (i : α) → NormedAddCommGroup (E i)] [inst_1 : DecidableEq α]
{F : Type u_5} [inst_2 : AddCommMonoid F] [inst_3 : TopologicalSpace F] [T2Space F] [inst_5 : Fact (1 ≤ p)]
{hp : p ≠ ⊤} {f g : ↥(lp E p) →ₜ+ F},
f = g ↔ ∀ (i : α), f.comp (lp.singleContinuousAddMonoidHom E p i) = g.comp (lp.singleContinuousAddMonoidHom E p i)- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- AddCommMonoidstatement and proof · cited by 12,281
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- AddSubgroupstatement · cited by 3,232
- Factstatement and proof · cited by 2,726
- T2Spacestatement and proof · cited by 1,351
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
- ContinuousAddMonoidHomstatement and proof · cited by 77
- ContinuousAddMonoidHom.compstatement and proof · cited by 10
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.