Theorems · Theorem · sequences and series
summableLocallyUniformly_iff_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
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- HasSumLocallyUniformlystatement · cited by 16
- SummableLocallyUniformlystatement · cited by 7
- HasSumLocallyUniformly.summableLocallyUniformlyproof · cited by 2
- SummableLocallyUniformly.hasSumLocallyUniformlyproof · cited by 1
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