Theorems · Theorem · measure theory
MeasureTheory.integral_norm_eq_lintegral_enorm
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {P : Type u_7} [inst : NormedAddCommGroup P]
{f : α → P}, MeasureTheory.AEStronglyMeasurable f μ → ∫ (x : α), ‖f x‖ ∂μ = (∫⁻ (x : α), ‖f x‖ₑ ∂μ).toReal- Cited by
- 3 results in Mathlib
- Foundations
- Depth 254 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.
Cites14
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Norm.normstatement · cited by 5,413
- MeasureTheory.integralstatement · cited by 1,779
- Filter.univ_mem'proof · cited by 1,672
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- ENNReal.toRealstatement and proof · cited by 859
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- ENorm.enormstatement and proof · cited by 715
- ofReal_normproof · cited by 39
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.ofReal_integral_norm_eq_lintegral_enormproof · cited by 5
- MeasureTheory.tendsto_integral_norm_approxOn_subproof · cited by 1
- IntervalIntegrable.absolutelyContinuousOnInterval_intervalIntegralproof · cited by 1