Theorems · Definition · sequences and series
SummableUniformly
{α : Type u_1} → {β : Type u_2} → {ι : Type u_3} → [AddCommMonoid α] → (ι → β → α) → [UniformSpace α] → PropSummableUniformly f means that there is some infinite sum to which
f converges uniformly. Use fun x ↦ ∑' i, f i x to get the product function.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 70 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- SummationFilter.unconditionalproof · cited by 2,068
- UniformSpacestatement and proof · cited by 2,040
- Summableproof · cited by 778
- UniformFun.ofFunproof · cited by 78
Cited by7
Results whose statement or proof uses this declaration.
- HasSumUniformly.summableUniformlystatement · cited by 2
- SummableUniformly.existsstatement and proof · cited by 2
- summableUniformlyOn_univ_iffstatement · cited by 1
- SummableUniformly.summableUniformlyOnstatement and proof · cited by 1
- SummableUniformly.hasSumUniformlystatement and proof · cited by 1
- SummableUniformly.summablestatement and proof · cited by 0
- summableUniformly_iff_hasSumUniformlystatement · cited by 0