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Theorems · Theorem · approximation theory

Asymptotics.IsBigO.const_mul_left

∀ {α : Type u_1} {F : Type u_4} {R : Type u_13} [inst : Norm F] [inst_1 : SeminormedRing R] {g : α → F} {l : Filter α}
  {f : α → R}, f =O[l] g → ∀ (c' : R), (fun x => c' * f x) =O[l] g
Defined in
Mathlib.Analysis.Asymptotics.Defs
Cited by
16 results in Mathlib
Foundations
Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormSeminormedRing

Around this declaration

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

Complex.tsum_exp_neg_quadratic · cited by 3Complex.tsum_exp_neg_quad…HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal · cited by 3HasFPowerSeriesWithinOnBa…NormedRing.inverse_add_norm_diff_nth_order · cited by 2NormedRing.inverse_add_no…ContinuousLinearMap.bilinear_hasTemperateGrowth · cited by 2ContinuousLinearMap.bilin…FormalMultilinearSeries.taylorComp_sub_taylorComp_isBigO · cited by 2FormalMultilinearSeries.t…HurwitzKernelBounds.isBigO_atTop_F_nat_one · cited by 2HurwitzKernelBounds.isBig…WeakFEPair.hf_zero' · cited by 1WeakFEPair.hf_zero'Real.isBigO_logb_const_mul_log_atTop · cited by 1Real.isBigO_logb_const_mu…Chebyshev.integral_one_div_log_sq_isBigO · cited by 1Chebyshev.integral_one_di…UpperHalfPlane.IsBoundedAtImInfty.slash · cited by 1IsBoundedAtImInfty.slashComplex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleO · cited by 1Complex.dist_le_mul_div_p…Polynomial.isBigO_cobounded_of_degree_le · cited by 0Polynomial.isBigO_cobound…HurwitzZeta.isBigO_atTop_cosKernel_sub · cited by 0HurwitzZeta.isBigO_atTop_…HurwitzZeta.isBigO_atTop_sinKernel · cited by 0HurwitzZeta.isBigO_atTop_…Real.isBigO_logb_log · cited by 0Real.isBigO_logb_logReal · cited by 25697RealFilter · cited by 8121FilterNorm · cited by 512NormAsymptotics.IsBigO · cited by 506Asymptotics.IsBigOSeminormedRing · cited by 446SeminormedRingAsymptotics.IsBigOWith · cited by 187Asymptotics.IsBigOWithAsymptotics.IsBigOWith.isBigO · cited by 40IsBigOWith.isBigOAsymptotics.IsBigO.isBigOWith · cited by 21IsBigO.isBigOWithAsymptotics.IsBigOWith.const_mul_left · cited by 1IsBigOWith.const_mul_leftIsBigO.const_mul_leftCITED BYCITES

Cites9

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Cited by16

Results whose statement or proof uses this declaration.