Theorems · Theorem · measure theory
MeasureTheory.memLp_indicator_const
∀ {α : Type u_1} {E : Type u_4} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup E]
{s : Set α} (p : ENNReal),
MeasurableSet s → ∀ (c : E), c = 0 ∨ μ s ≠ ⊤ → MeasureTheory.MemLp (s.indicator fun x => c) p μ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 209 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · 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
- Top.topstatement and proof · cited by 9,680
- MeasurableSetstatement and proof · cited by 3,075
- Factproof · cited by 2,726
- Set.indicatorstatement · cited by 723
- MeasureTheory.MemLpstatement · cited by 457
- Ne.lt_topproof · cited by 161
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.indicatorConstLp_coeFnproof · cited by 15
- MeasureTheory.MemLp.induction_stronglyMeasurableproof · cited by 1