Theorems · Definition · number theory
addWellApproximable
(A : Type u_1) → [SeminormedAddGroup A] → (ℕ → ℝ) → Set A
In a seminormed additive group A, given a sequence of
distances δ₁, δ₂, ..., addWellApproximable A δ is the limsup as n → ∞ of the sets
approxAddOrderOf A n δₙ. Thus, it is the set of points that lie in infinitely many of the sets
approxAddOrderOf A n δₙ.
- Defined in
- Mathlib.NumberTheory.WellApproximable
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Filter.atTopproof · cited by 2,405
- SeminormedAddGroupstatement and proof · cited by 331
- Filter.blimsupproof · cited by 40
- approxAddOrderOfproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- UnitAddCircle.mem_addWellApproximable_iffstatement · cited by 0
- AddCircle.addWellApproximable_ae_empty_or_univstatement and proof · cited by 0
- mem_add_wellApproximable_iffstatement · cited by 0