Theorems · Definition · sequences and series
HasSumUniformlyOn
{α : Type u_1} →
{β : Type u_2} → {ι : Type u_3} → [AddCommMonoid α] → (ι → β → α) → (β → α) → Set β → [UniformSpace α] → PropHasSumUniformlyOn f g s means that the (potentially infinite) sum ∑' i, f i b
for b : β converges uniformly on s to g.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidUniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- AddCommMonoidstatement and proof · cited by 12,281
- SummationFilter.unconditionalproof · cited by 2,068
- UniformSpacestatement and proof · cited by 2,040
- HasSumproof · cited by 518
- UniformOnFun.ofFunproof · cited by 63
Cited by24
Results whose statement or proof uses this declaration.
- hasSumUniformlyOn_iff_tendstoUniformlyOnstatement · cited by 12
- HasSumUniformlyOn.tendstoUniformlyOnstatement · cited by 6
- SummableUniformlyOn.existsstatement · cited by 5
- SummableUniformlyOn.hasSumUniformlyOnstatement and proof · cited by 4
- HasSumUniformlyOn.hasSumstatement and proof · cited by 3
- HasSumUniformlyOn.summableUniformlyOnstatement and proof · cited by 3
- hasSumUniformlyOn_univ_iffstatement · cited by 2
- hasSumLocallyUniformlyOn_of_of_forall_exists_nhdsstatement and proof · cited by 1
- hasSumLocallyUniformly_of_of_forall_exists_nhdsstatement and proof · cited by 1
- hasProdUniformlyOn_of_clogproof · cited by 1
- HasSumUniformly.hasSumUniformlyOnstatement · cited by 1
- HasSumUniformlyOn.monostatement and proof · cited by 1