Theorems · Definition · functional analysis
MeasureTheory.Lp
{α : Type u_7} →
(E : Type u_6) →
{m : MeasurableSpace α} →
[inst : NormedAddCommGroup E] →
ENNReal → (μ : autoParam (MeasureTheory.Measure α) MeasureTheory.Lp._auto_1) → AddSubgroup (α →ₘ[μ] E)Lp space
- Cited by
- 715 results in Mathlib
- Foundations
- Depth 220 from the axioms, rests on 6,085 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Top.topproof · cited by 9,680
- Set.ofPredproof · cited by 6,101
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.AEEqFunstatement and proof · cited by 856
- MeasureTheory.AEEqFun.castproof · cited by 380
- MeasureTheory.eLpNormproof · cited by 329
Cited by798
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.simpleFuncstatement and proof · cited by 122
- MeasureTheory.MemLp.toLpstatement · cited by 70
- MeasureTheory.indicatorConstLpstatement · cited by 64
- MeasureTheory.Integrable.toL1statement · cited by 58
- MeasureTheory.Lp.simpleFunc.toSimpleFuncstatement and proof · cited by 46
- MeasureTheory.lpMeasstatement and proof · cited by 46
- MeasureTheory.L1.setToL1statement · cited by 44
- MeasureTheory.condExpL2statement · cited by 36
- MeasureTheory.Lp.memLpstatement and proof · cited by 35
- MeasureTheory.MemLp.coeFn_toLpstatement · cited by 35
- MeasureTheory.L1.SimpleFunc.setToL1SCLMstatement · cited by 30
- MeasureTheory.Lp.simpleFunc.modulestatement and proof · cited by 29
Showing the 200 most cited of 798.