Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.memLp_approxOn_range
∀ {β : Type u_2} {E : Type u_4} [inst : MeasurableSpace β] [inst_1 : MeasurableSpace E] [inst_2 : NormedAddCommGroup E]
{p : ENNReal} [inst_3 : BorelSpace E] {f : β → E} {μ : MeasureTheory.Measure β} (fmeas : Measurable f)
[inst_4 : TopologicalSpace.SeparableSpace ↑(Set.range f ∪ {0})],
MeasureTheory.MemLp f p μ →
∀ (n : ℕ), MeasureTheory.MemLp (⇑(MeasureTheory.SimpleFunc.approxOn f fmeas (Set.range f ∪ {0}) 0 ⋯ n)) p μ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- 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
- Set.Elemstatement and proof · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- BorelSpacestatement and proof · cited by 1,602
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.MemLpstatement and proof · cited by 457
- MeasureTheory.SimpleFuncstatement · cited by 411
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.MemLp.finStronglyMeasurable_of_stronglyMeasurableproof · cited by 2
- MeasureTheory.MemLp.exists_simpleFunc_eLpNorm_sub_ltproof · cited by 2
- MeasureTheory.Lp.simpleFunc.isDenseEmbeddingproof · cited by 1
- MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lpstatement and proof · cited by 1