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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
Assumes
NormNormSeminormedAddCommGroup

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Asymptotics.IsEquivalent.symm · cited by 20IsEquivalent.symmAsymptotics.IsEquivalent.trans · cited by 5IsEquivalent.transHasFDerivWithinAt.tendsto_nhdsWithin_nhdsNE · cited by 4HasFDerivWithinAt.tendsto…Asymptotics.IsLittleO.const_mul_right · cited by 4IsLittleO.const_mul_rightAsymptotics.IsLittleO.of_const_mul_right · cited by 3IsLittleO.of_const_mul_ri…HasFDerivAt.comp_semilinear · cited by 3HasFDerivAt.comp_semiline…intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae · cited by 2intervalIntegral.integral…intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae · cited by 2intervalIntegral.integral…Complex.hasSum_taylorSeries_log · cited by 2Complex.hasSum_taylorSeri…Asymptotics.IsLittleO.trans_isTheta · cited by 2IsLittleO.trans_isThetaAsymptotics.isLittleO_const_iff_isLittleO_one · cited by 1Asymptotics.isLittleO_con…Asymptotics.isLittleO_const_mul_right_iff · cited by 1Asymptotics.isLittleO_con…Asymptotics.IsLittleO.const_mul_right' · cited by 1IsLittleO.const_mul_right'Asymptotics.IsLittleO.tendsto_zero_of_tendsto · cited by 1IsLittleO.tendsto_zero_of…Convex.taylor_approx_two_segment · cited by 1Convex.taylor_approx_two_…Real · cited by 25697RealFilter · cited by 8121FilterSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupNorm · cited by 512NormAsymptotics.IsBigO · cited by 506Asymptotics.IsBigOAsymptotics.IsLittleO · cited by 375Asymptotics.IsLittleOAsymptotics.IsBigOWith · cited by 187Asymptotics.IsBigOWithAsymptotics.IsBigO.exists_pos · cited by 19IsBigO.exists_posAsymptotics.IsLittleO.trans_isBigOWith · cited by 4IsLittleO.trans_isBigOWithIsLittleO.trans_isBigOCITED BYCITES

Cites9

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Cited by19

Results whose statement or proof uses this declaration.