Theorems · Theorem · functional analysis
MeasureTheory.Integrable.norm_toL1_eq_lintegral_enorm
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
(f : α → β) (hf : MeasureTheory.Integrable f μ), ‖MeasureTheory.Integrable.toL1 f hf‖ = (∫⁻ (a : α), ‖f a‖ₑ ∂μ).toReal- Cited by
- 2 results in Mathlib
- Foundations
- Depth 225 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · 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
- Norm.normstatement · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- ENNReal.toRealstatement and proof · cited by 859
- MeasureTheory.AEEqFunstatement · cited by 856
- ENorm.enormstatement and proof · cited by 715
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.enorm_setToFun_leproof · cited by 4
- MeasureTheory.norm_setToFun_le_toRealproof · cited by 2