Theorems · Theorem · complex analysis
Filter.tendsto_ofReal_iff
∀ {α : Type u_2} {l : Filter α} {f : α → ℝ} {x : ℝ},
Filter.Tendsto (fun x => ↑(f x)) l (nhds ↑x) ↔ Filter.Tendsto f l (nhds x)- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Complexstatement · cited by 5,565
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Complex.ofRealstatement · cited by 1,654
- IsUniformEmbedding.isClosedEmbeddingproof · cited by 7
- Topology.IsClosedEmbedding.tendsto_nhds_iffproof · cited by 4
- Complex.isUniformEmbedding_ofRealproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Filter.Tendsto.ofRealproof · cited by 4
- Real.tendsto_one_add_rpow_exp_of_tendstoproof · cited by 2
- Real.tendsto_mul_log_one_add_of_tendstoproof · cited by 2
- ProbabilityTheory.eqOn_complexMGF_of_mgf'proof · cited by 1
- tendsto_sub_mul_tsum_nat_rpowproof · cited by 0