Theorems · Theorem · complex analysis
CircleIntegrable.finsum
∀ {E : Type u_1} [inst : NormedAddCommGroup E] {c : ℂ} {R : ℝ} {ι : Type u_3} {f : ι → ℂ → E},
(∀ (i : ι), CircleIntegrable (f i) c R) → CircleIntegrable (∑ᶠ (i : ι), f i) c Rfinsums of circle integrable functions are circle integrable.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 248 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 and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Complexstatement and proof · cited by 5,565
- Set.Finiteproof · cited by 1,814
- Function.supportproof · cited by 610
- Set.Finite.toFinsetproof · cited by 351
- finsumstatement · cited by 286
- CircleIntegrablestatement and proof · cited by 86
- finsum_eq_sumproof · cited by 17
- finsum_of_infinite_supportproof · cited by 10
- circleIntegrable_constproof · cited by 7
- CircleIntegrable.sumproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- MeromorphicOn.circleIntegrable_log_normproof · cited by 11
- circleIntegrable_log_norm_factorizedRationalproof · cited by 1