Theorems · Theorem · functional analysis
lp.isLUB_norm
∀ {α : Type u_3} {E : α → Type u_4} [inst : (i : α) → NormedAddCommGroup (E i)] [Nonempty α] (f : ↥(lp E ⊤)),
IsLUB (Set.range fun i => ‖↑f i‖) ‖f‖- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroupNonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Norm.normstatement and proof · cited by 5,413
- Set.rangestatement and proof · cited by 4,705
- AddSubgroupstatement · cited by 3,232
- IsLUBstatement and proof · cited by 280
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
- lp.memℓpproof · cited by 11
- isLUB_ciSupproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- lp.norm_apply_le_normproof · cited by 6
- lp.norm_nonneg'proof · cited by 6
- lp.norm_le_of_forall_le'proof · cited by 1
- lp.norm_const_smul_leproof · cited by 1
- lp.norm_eq_zero_iffproof · cited by 0
- lp.norm_negproof · cited by 0