Theorems · Theorem · order theory
Filter.limsup_nat_add
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] (f : ℕ → α) (k : ℕ),
Filter.limsup (fun i => f (i + k)) Filter.atTop = Filter.limsup f Filter.atTop- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ConditionallyCompleteLattice
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.
- Filter.atTopstatement · cited by 2,405
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.limsupstatement · cited by 226
- Filter.liminf_nat_addproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_mem_limsup_atTop_iffproof · cited by 1