Theorems · Theorem · functional analysis
eventually_norm_pow_le
∀ {α : Type u_2} [inst : SeminormedRing α] (a : α), ∀ᶠ (n : ℕ) in Filter.atTop, ‖a ^ n‖ ≤ ‖a‖ ^ n- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRing
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 · cited by 25,697
- Norm.normstatement · cited by 5,413
- Filter.Eventuallystatement · cited by 3,134
- Filter.atTopstatement · cited by 2,405
- SeminormedRingstatement and proof · cited by 446
- Filter.eventually_atTopproof · cited by 112
- norm_pow_le'proof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- tendsto_pow_atTop_nhds_zero_of_norm_lt_oneproof · cited by 13
- isLittleO_pow_const_mul_const_pow_const_pow_of_norm_ltproof · cited by 2
- summable_norm_mul_geometric_of_norm_lt_oneproof · cited by 2
- summable_norm_mul_geometric_of_norm_lt_one'proof · cited by 1