Theorems · Theorem · general topology
Filter.tendsto_add_atTop_iff_nat
∀ {α : Type u_3} {f : ℕ → α} {l : Filter α} (k : ℕ),
Filter.Tendsto (fun n => f (n + k)) Filter.atTop l ↔ Filter.Tendsto f Filter.atTop l- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Filter.tendsto_map'_iffproof · cited by 50
- Filter.map_add_atTop_eq_natproof · cited by 5
Cited by23
Results whose statement or proof uses this declaration.
- NormedSpace.expSeries_radius_eq_topproof · cited by 27
- tendsto_pow_atTop_nhds_zero_of_lt_oneproof · cited by 18
- MeasureTheory.tendsto_setToFun_filter_of_dominated_convergenceproof · cited by 6
- tendsto_one_div_add_atTop_nhds_zero_natproof · cited by 4
- Filter.exists_seq_monotone_tendsto_atTop_atTopproof · cited by 3
- NNReal.agm_eq_agm_agmSequences_fst_agmSequences_sndproof · cited by 3
- Real.tendsto_atTop_csInf_of_antitoneOn_bddBelow_nat_Iciproof · cited by 3
- MeasureTheory.isSigmaSubadditive_of_addContent_iUnion_eq_tsumproof · cited by 2
- MeasureTheory.addContent_iUnion_eq_sum_of_tendsto_zeroproof · cited by 2
- CircleDeg1Lift.tendsto_translation_number'proof · cited by 2
- MeasureTheory.tendsto_lintegral_filter_of_dominated_convergence'proof · cited by 2
- CircleDeg1Lift.tendsto_translation_number₀proof · cited by 2