Theorems · Theorem · functional analysis
NormedSpace.exp_sum
∀ {𝔸 : Type u_2} [inst : NormedCommRing 𝔸] [NormedAlgebra ℚ 𝔸] [CompleteSpace 𝔸] {ι : Type u_3} (s : Finset ι)
(f : ι → 𝔸), NormedSpace.exp (∑ i ∈ s, f i) = ∏ i ∈ s, NormedSpace.exp (f i)A version of NormedSpace.exp_sum_of_commute for a commutative Banach-algebra.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Finset.sumstatement · cited by 5,195
- CompleteSpacestatement and proof · cited by 2,532
- Finset.prodstatement and proof · cited by 2,356
- NormedAlgebrastatement and proof · cited by 1,165
- NormedCommRingstatement and proof · cited by 218
- NormedSpace.expstatement and proof · cited by 157
- Commute.allproof · cited by 119
- Finset.noncommProd_eq_prodproof · cited by 3
- NormedSpace.exp_sum_of_commuteproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- HasSum.expproof · cited by 0