Theorems · Theorem · measure theory
ENNReal.ae_eq_zero_of_lintegral_rpow_eq_zero
∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {p : ℝ},
0 ≤ p → ∀ {f : α → ENNReal}, AEMeasurable f μ → ∫⁻ (a : α), f a ^ p ∂μ = 0 → f =ᵐ[μ] 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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.
- 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
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- LT.lt.ne'proof · cited by 1,417
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- AEMeasurablestatement and proof · cited by 840
- pos_iff_ne_zeroproof · cited by 180
Cited by1
Results whose statement or proof uses this declaration.
- ENNReal.lintegral_mul_eq_zero_of_lintegral_rpow_eq_zeroproof · cited by 1