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Theorems · Theorem · functional analysis

MeasureTheory.Lp.coeFn_add

∀ {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
12 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.condExp_add · cited by 11MeasureTheory.condExp_addMeasureTheory.Lp.dist_eq_eLpNorm_neg_add · cited by 2Lp.dist_eq_eLpNorm_neg_addMeasureTheory.MemLp.induction_stronglyMeasurable · cited by 1MemLp.induction_stronglyM…MeasureTheory.lpMeasSubgroupToLpTrim_add · cited by 1MeasureTheory.lpMeasSubgr…MeasureTheory.condExpIndL1Fin_add · cited by 1MeasureTheory.condExpIndL…MeasureTheory.condExpIndL1Fin_disjoint_union · cited by 1MeasureTheory.condExpIndL…ContinuousLinearMap.add_compLp · cited by 1ContinuousLinearMap.add_c…MeasureTheory.aestronglyMeasurable_condExpL1CLM · cited by 1MeasureTheory.aestronglyM…MeasureTheory.indicatorConstLp_disjoint_union · cited by 1MeasureTheory.indicatorCo…MeasureTheory.Lp.simpleFunc.add_toSimpleFunc · cited by 1simpleFunc.add_toSimpleFu…MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top · cited by 1MeasureTheory.setIntegral…MeasureTheory.Lp_toLp_restrict_add · cited by 0MeasureTheory.Lp_toLp_res…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_add · cited by 6AEEqFun.coeFn_addLp.coeFn_addCITED BYCITES

Cites11

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Cited by12

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