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- 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.Lpstatement and proof · cited by 715
- MeasureTheory.AEEqFun.caststatement · cited by 380
- MeasureTheory.AEEqFun.coeFn_addproof · cited by 6
Cited by12
Results whose statement or proof uses this declaration.
- MeasureTheory.condExp_addproof · cited by 11
- MeasureTheory.Lp.dist_eq_eLpNorm_neg_addproof · cited by 2
- MeasureTheory.MemLp.induction_stronglyMeasurableproof · cited by 1
- MeasureTheory.lpMeasSubgroupToLpTrim_addproof · cited by 1
- MeasureTheory.condExpIndL1Fin_addproof · cited by 1
- MeasureTheory.condExpIndL1Fin_disjoint_unionproof · cited by 1
- ContinuousLinearMap.add_compLpproof · cited by 1
- MeasureTheory.aestronglyMeasurable_condExpL1CLMproof · cited by 1
- MeasureTheory.indicatorConstLp_disjoint_unionproof · cited by 1
- MeasureTheory.Lp.simpleFunc.add_toSimpleFuncproof · cited by 1
- MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_topproof · cited by 1
- MeasureTheory.Lp_toLp_restrict_addproof · cited by 0