Theorems · Theorem · approximation theory
Asymptotics.IsLittleO.trans_isBigO
∀ {α : Type u_1} {E : Type u_3} {F : Type u_4} {G' : Type u_8} [inst : Norm E] [inst_1 : Norm F]
[inst_2 : SeminormedAddCommGroup G'] {l : Filter α} {f : α → E} {g : α → F} {k : α → G'},
f =o[l] g → g =O[l] k → f =o[l] k- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement and proof · cited by 506
- Asymptotics.IsLittleOstatement and proof · cited by 375
- Asymptotics.IsBigOWithproof · cited by 187
- Asymptotics.IsBigO.exists_posproof · cited by 19
- Asymptotics.IsLittleO.trans_isBigOWithproof · cited by 4
Cited by19
Results whose statement or proof uses this declaration.
- Asymptotics.IsEquivalent.symmproof · cited by 20
- Asymptotics.IsEquivalent.transproof · cited by 5
- HasFDerivWithinAt.tendsto_nhdsWithin_nhdsNEproof · cited by 4
- Asymptotics.IsLittleO.const_mul_rightproof · cited by 4
- Asymptotics.IsLittleO.of_const_mul_rightproof · cited by 3
- HasFDerivAt.comp_semilinearproof · cited by 3
- intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_aeproof · cited by 2
- intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_aeproof · cited by 2
- Complex.hasSum_taylorSeries_logproof · cited by 2
- Asymptotics.IsLittleO.trans_isThetaproof · cited by 2
- Asymptotics.isLittleO_const_iff_isLittleO_oneproof · cited by 1
- Asymptotics.isLittleO_const_mul_right_iffproof · cited by 1