Theorems · Theorem · sequences and series
Summable.tendsto_atTop_of_pos
∀ {α : Type u_3} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [inst_3 : TopologicalSpace α]
[OrderTopology α] {f : ℕ → α}, Summable f⁻¹ → (∀ (n : ℕ), 0 < f n) → Filter.Tendsto f Filter.atTop Filter.atTop- 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.
Cites15
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
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- Filter.Tendstostatement · cited by 3,814
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement · cited by 2,405
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- OrderTopologystatement and proof · cited by 1,355
- Summablestatement and proof · cited by 778
- Filter.Eventually.of_forallproof · cited by 526
- inv_invproof · cited by 494
- inv_posproof · cited by 124
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.exists_subset_restrict_nonposproof · cited by 1