Theorems · Theorem · functional analysis
lp.norm_eq_card_dsupport
∀ {α : Type u_3} {E : α → Type u_4} [inst : (i : α) → NormedAddCommGroup (E i)] (f : ↥(lp E 0)), ‖f‖ = ↑⋯.toFinset.card- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 216 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- ENNRealstatement · cited by 9,879
- Set.ofPredstatement · cited by 6,101
- Norm.normstatement · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- Finset.cardstatement · cited by 2,327
- Set.Finite.toFinsetstatement · cited by 351
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
- lp.memℓpstatement · cited by 11
- Memℓp.finite_dsupportstatement · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- lp.norm_nonneg'proof · cited by 6
- lp.norm_zeroproof · cited by 3
- lp.norm_toNormproof · cited by 0
- lp.norm_eq_zero_iffproof · cited by 0
- equiv_lpPiLp_normproof · cited by 0
- lp.norm_negproof · cited by 0