Theorems · Theorem · functional analysis
lp.coeFn_sum
∀ {α : Type u_3} {E : α → Type u_4} {p : ENNReal} [inst : (i : α) → NormedAddCommGroup (E i)] {ι : Type u_5}
(f : ι → ↥(lp E p)) (s : Finset ι), ↑(∑ i ∈ s, f i) = ∑ i ∈ s, ↑(f i)- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 213 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.
Cites8
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
- Finsetstatement and proof · cited by 13,712
- ENNRealstatement and proof · cited by 9,879
- Finset.sumstatement · cited by 5,195
- AddSubgroupstatement · cited by 3,232
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
- AddSubgroup.val_finsetSumproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- lp.norm_sub_norm_compl_sub_singleproof · cited by 1
- lp.norm_sum_singleproof · cited by 0