Theorems · Theorem · functional analysis
lp.ext_iff
∀ {α : Type u_3} {E : α → Type u_4} {p : ENNReal} [inst : (i : α) → NormedAddCommGroup (E i)] {f g : ↥(lp E p)},
f = g ↔ ↑f = ↑g- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- ENNRealstatement and proof · cited by 9,879
- AddSubgroupstatement · cited by 3,232
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
- lp.extproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- lp.eq_zero_iff_coeFn_eq_zeroproof · cited by 0