Theorems · Theorem · measure theory
NNReal.not_summable_iff_tendsto_nat_atTop
∀ {f : ℕ → NNReal}, ¬Summable f ↔ Filter.Tendsto (fun n => ∑ i ∈ Finset.range n, f i) Filter.atTop Filter.atTop- Cited by
- 2 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.sumstatement and proof · cited by 5,195
- NNRealstatement and proof · cited by 4,310
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Finset.rangestatement and proof · cited by 1,341
- Summablestatement and proof · cited by 778
- Filter.Tendsto.compproof · cited by 560
- HasSumproof · cited by 518
- Filter.tendsto_finset_rangeproof · cited by 15
- not_tendsto_nhds_of_tendsto_atTopproof · cited by 7
- tendsto_atTop_of_monotoneproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- not_summable_iff_tendsto_nat_atTop_of_nonnegproof · cited by 2
- NNReal.summable_iff_not_tendsto_nat_atTopproof · cited by 1