Theorems · Theorem · measure theory
MeasureTheory.eLpNorm_one_le_of_le
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ} {r : NNReal},
MeasureTheory.Integrable f μ →
0 ≤ ∫ (x : α), f x ∂μ → (∀ᵐ (ω : α) ∂μ, f ω ≤ ↑r) → MeasureTheory.eLpNorm f 1 μ ≤ 2 * μ Set.univ * ↑r- Cited by
- 1 results in Mathlib
- Foundations
- Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites71
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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- 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
- Norm.normproof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- Set.univstatement and proof · cited by 3,945
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNorm_one_le_of_le'proof · cited by 1