Theorems · Theorem · approximation theory
Asymptotics.isBigO_const_mul_self
∀ {α : Type u_1} {R : Type u_13} [inst : SeminormedRing R] (c : R) (f : α → R) (l : Filter α),
(fun x => c * f x) =O[l] f- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 105 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Asymptotics.IsBigOstatement · cited by 506
- SeminormedRingstatement and proof · cited by 446
- Asymptotics.IsBigOWith.isBigOproof · cited by 40
- Asymptotics.isBigOWith_const_mul_selfproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- Asymptotics.IsLittleO.const_mul_leftproof · cited by 8
- Asymptotics.IsLittleO.of_const_mul_rightproof · cited by 3
- Convex.taylor_approx_two_segmentproof · cited by 1
- Summable.mul_tendsto_constproof · cited by 1
- Chebyshev.integral_one_div_log_sq_isBigOproof · cited by 1
- Function.locallyFinsuppWithin.logCounting_single_isBigO_logproof · cited by 1
- Asymptotics.isBigO_const_mul_left_iffproof · cited by 1
- Asymptotics.isLittleO_const_mul_left_iffproof · cited by 1