Theorems · Theorem · sequences and series
Multipliable.tendsto_cofinite_one
∀ {α : Type u_1} {G : Type u_4} [inst : TopologicalSpace G] [inst_1 : CommGroup G] [IsTopologicalGroup G] {f : α → G},
Multipliable f → Filter.Tendsto f Filter.cofinite (nhds 1)Product divergence test: if f is unconditionally multipliable, then f x tends to one along
cofinite.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetproof · cited by 13,712
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Finset.prodproof · cited by 2,356
- Disjointproof · cited by 2,201
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- CommGroupstatement and proof · cited by 990
- Filter.Eventually.monoproof · cited by 646
- IsTopologicalGroupstatement and proof · cited by 469
- Filter.cofinitestatement · cited by 251
Cited by6
Results whose statement or proof uses this declaration.
- IsUltrametricDist.norm_tprod_leproof · cited by 2
- Multipliable.hasFiniteMulSupport_of_discreteTopologyproof · cited by 1
- NonarchimedeanGroup.multipliable_iff_tendsto_cofinite_oneproof · cited by 0
- Multipliable.countable_mulSupportproof · cited by 0
- Multipliable.tendsto_atTop_oneproof · cited by 0
- multipliable_const_iffproof · cited by 0