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Theorems · Theorem · approximation theory

Asymptotics.IsBigO.mono

∀ {α : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Norm E] [inst_1 : Norm F] {f : α → E} {g : α → F}
  {l l' : Filter α}, f =O[l'] g → l ≤ l' → f =O[l] g
Defined in
Mathlib.Analysis.Asymptotics.Defs
Cited by
16 results in Mathlib
Foundations
Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormNorm

Around this declaration

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

HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_sub · cited by 2HasFPowerSeriesWithinAt.i…PhragmenLindelof.right_half_plane_of_tendsto_zero_on_real · cited by 2PhragmenLindelof.right_ha…Asymptotics.isBigO_sup · cited by 2Asymptotics.isBigO_supFunction.Periodic.exp_decay_sub_of_bounded_at_inf · cited by 2Periodic.exp_decay_sub_of…log_deriv_riemannZeta_add_inv_sub_sub_isBigO · cited by 1log_deriv_riemannZeta_add…log_riemannZeta_add_log_sub_isBigO_ofReal · cited by 1log_riemannZeta_add_log_s…not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_punctured · cited by 1not_intervalIntegrable_of…not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_within_sdiff_singleton · cited by 1not_intervalIntegrable_of…inv_riemannZeta_sub_sub_isBigO · cited by 1inv_riemannZeta_sub_sub_i…Asymptotics.IsTheta.mono · cited by 1IsTheta.monoAsymptotics.isBigO_cofinite_iff · cited by 1Asymptotics.isBigO_cofini…DirichletCharacter.LFunction_isBigO_horizontal · cited by 0DirichletCharacter.LFunct…deriv_riemannZeta_add_inv_sub_sq_bounded · cited by 0deriv_riemannZeta_add_inv…circleIntegrable_sub_zpow_iff · cited by 0circleIntegrable_sub_zpow…Asymptotics.isBigO_one_nhds_ne_iff · cited by 0Asymptotics.isBigO_one_nh…Real · cited by 25697RealFilter · cited by 8121FilterNorm · cited by 512NormAsymptotics.IsBigO · cited by 506Asymptotics.IsBigOAsymptotics.IsBigOWith · cited by 187Asymptotics.IsBigOWithAsymptotics.IsBigO.isBigOWith · cited by 21IsBigO.isBigOWithAsymptotics.isBigO_iff_isBigOWith · cited by 8Asymptotics.isBigO_iff_is…Asymptotics.IsBigOWith.mono · cited by 2IsBigOWith.monoIsBigO.monoCITED BYCITES

Cites8

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Cited by16

Results whose statement or proof uses this declaration.