Theorems · Theorem · functional analysis
eventually_cobounded_le_norm
∀ {E : Type u_2} [inst : SeminormedAddGroup E] (a : ℝ), ∀ᶠ (x : E) in Bornology.cobounded E, a ≤ ‖x‖- Defined in
- Mathlib.Analysis.Normed.Group.Bounded
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 118 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.
Cites7
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
- Norm.normstatement · cited by 5,413
- Filter.Eventuallystatement · cited by 3,134
- SeminormedAddGroupstatement and proof · cited by 331
- Bornology.coboundedstatement · cited by 162
- Filter.Tendsto.eventually_ge_atTopproof · cited by 22
- tendsto_norm_cobounded_atTopproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- PhragmenLindelof.isBigO_sub_exp_rpowproof · cited by 5
- PhragmenLindelof.eq_zero_on_right_half_plane_of_superexponential_decayproof · cited by 1