Theorems · Theorem · sequences and series
SummableLocallyUniformly.hasSumLocallyUniformly
∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} [inst : AddCommMonoid α] {f : ι → β → α} [inst_1 : UniformSpace α]
[inst_2 : TopologicalSpace β], SummableLocallyUniformly f → HasSumLocallyUniformly f fun x => ∑' (i : ι), f i x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommMonoidstatement and proof · cited by 12,281
- SummationFilter.unconditionalstatement · cited by 2,068
- UniformSpacestatement and proof · cited by 2,040
- tsumstatement · cited by 1,148
- Summable.hasSumproof · cited by 184
- HasSum.summableproof · cited by 98
- HasSumLocallyUniformlystatement and proof · cited by 16
- tendsto_nhds_unique_inseparableproof · cited by 10
- SummableLocallyUniformlystatement and proof · cited by 7
- HasSumLocallyUniformly.hasSumproof · cited by 4
- TendstoLocallyUniformly.congr_inseparable_rightproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- summableLocallyUniformly_iff_hasSumLocallyUniformlyproof · cited by 0