Theorems · Theorem · general topology
Filter.not_tendsto_iff_exists_frequently_notMem
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {l₁ : Filter α} {l₂ : Filter β},
¬Filter.Tendsto f l₁ l₂ ↔ ∃ s ∈ l₂, ∃ᶠ (x : α) in l₁, f x ∉ s- Defined in
- Mathlib.Order.Filter.Tendsto
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Filter.Tendstostatement · cited by 3,814
- Filter.Frequentlystatement and proof · cited by 414
Cited by3
Results whose statement or proof uses this declaration.
- Filter.tendsto_of_subseq_tendstoproof · cited by 3
- MeasureTheory.not_tendsto_diracProba_of_not_tendstoproof · cited by 1
- MeasureTheory.exists_seq_tendstoInMeasure_atTop_iffproof · cited by 0