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Theorems · Theorem · functional analysis

MeasureTheory.Lp.coeFn_sub

∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] (f g : ↥(MeasureTheory.Lp E p μ)), ↑↑(f - g) =ᵐ[μ] ↑↑f - ↑↑g
Defined in
Mathlib.MeasureTheory.Function.LpSpace.Basic
Cited by
13 results in Mathlib
Foundations
Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroup

Around this declaration

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

MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm' · cited by 5Lp.tendsto_Lp_iff_tendsto…MeasureTheory.integral_condExpL2_eq · cited by 3MeasureTheory.integral_co…MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq' · cited by 2Lp.ae_eq_of_forall_setInt…MeasureTheory.Lp.edist_dist · cited by 2Lp.edist_distMeasureTheory.continuous_L1_toL1 · cited by 1MeasureTheory.continuous_…LipschitzWith.norm_compLp_sub_le · cited by 1LipschitzWith.norm_compLp…MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm'' · cited by 0Lp.tendsto_Lp_iff_tendsto…MeasureTheory.Lp.cauchySeq_Lp_iff_cauchySeq_eLpNorm · cited by 0Lp.cauchySeq_Lp_iff_cauch…MeasureTheory.Lp.simpleFunc.sub_toSimpleFunc · cited by 0simpleFunc.sub_toSimpleFu…MeasureTheory.Lp.completeSpace_lp_of_cauchy_complete_eLpNorm · cited by 0Lp.completeSpace_lp_of_ca…MeasureTheory.L1.dist_eq_integral_dist · cited by 0L1.dist_eq_integral_distMeasureTheory.L1.norm_sub_eq_lintegral · cited by 0L1.norm_sub_eq_lintegralMeasureTheory.L1.ofReal_norm_sub_eq_lintegral · cited by 0L1.ofReal_norm_sub_eq_lin…NormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealAddSubgroup · cited by 3232AddSubgroupMeasureTheory.ae · cited by 2352MeasureTheory.aeFilter.EventuallyEq · cited by 1912Filter.EventuallyEqMeasureTheory.AEEqFun · cited by 856MeasureTheory.AEEqFunMeasureTheory.Lp · cited by 715MeasureTheory.LpMeasureTheory.AEEqFun.cast · cited by 380AEEqFun.castMeasureTheory.AEEqFun.coeFn_sub · cited by 1AEEqFun.coeFn_subLp.coeFn_subCITED BYCITES

Cites11

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Cited by13

Results whose statement or proof uses this declaration.