Theorems · Theorem · measure theory
MeasureTheory.L1.norm_eq_integral_norm
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {H : Type u_6} [inst : NormedAddCommGroup H]
(f : ↥(MeasureTheory.Lp H 1 μ)), ‖f‖ = ∫ (a : α), ‖↑↑f a‖ ∂μ- 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.
Cites24
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
- ENNRealstatement · cited by 9,879
- Top.topproof · cited by 9,680
- Norm.normstatement and proof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.integralstatement and proof · cited by 1,779
- MeasureTheory.lintegralproof · cited by 1,152
- ENNReal.toRealproof · cited by 859
- MeasureTheory.AEEqFunstatement and proof · cited by 856
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.norm_condExpIndL1Fin_leproof · cited by 1
- MeasureTheory.L1.dist_eq_integral_distproof · cited by 0
- MeasureTheory.L1.norm_of_fun_eq_integral_normproof · cited by 0